Congruence - Geometry
Card 0 of 956
Determine whether the statement is true or false:
In the figure 
, 
and 
and 
, therefore 
is a parallelogram.
Determine whether the statement is true or false:
In the figure
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Therefore, the statement is true.
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Therefore, the statement is true.
Compare your answer with the correct one above
Determine whether the statement is true or false:
In the figure 
, 
, 
, 
, and opposite side lengths are congruent, therefore 
is a parallelogram.
Determine whether the statement is true or false:
In the figure
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Since the angles given represent those in a parallelogram, and the opposite sides are congruent, that makes the figure a parallelogram.
Therefore, the statement is true.
Recall that a parallelogram is a special type of quadrilateral meaning, it is a shape that has four sides with opposite sides being parallel and congruent. Along with opposite sides being congruent, a parallelogram has two pairs of opposite angles that are congruent. Lastly, the diagonals of a parallelogram must bisect each other.
Since the angles given represent those in a parallelogram, and the opposite sides are congruent, that makes the figure a parallelogram.
Therefore, the statement is true.
Compare your answer with the correct one above
Fill in the blanks to the proof below. We are proving that the base angles of isosceles triangles, 
, are congruent. This is a proof of the isosceles triangle theorem.
Fill in the blanks to the proof below. We are proving that the base angles of isosceles triangles, 
Compare your answer with the correct one above
The triangle inequality theorem states that if you have a triangle 
then
Fill in the blanks for the proof of the theorem below using triangle 
To begin this proof we first must let there exist the triangle 
, where the length of 
and 
is a shared side between the two triangles.
The triangle inequality theorem states that if you have a triangle 
Fill in the blanks for the proof of the theorem below using triangle
To begin this proof we first must let there exist the triangle 
Follow the detailed proof below for an explanation.
To begin this proof we first must let there exist the triangle 
, where the length of 
and 
is a shared side between the two triangles.
Follow the detailed proof below for an explanation.
To begin this proof we first must let there exist the triangle 
Compare your answer with the correct one above
True or False: The SAS Theorem, ASA Theorem, SSS Theorem, and AA Theorem are all theorems that prove triangles to be congruent.
True or False: The SAS Theorem, ASA Theorem, SSS Theorem, and AA Theorem are all theorems that prove triangles to be congruent.
Three of these theorems do prove triangles to be congruent; SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and SSS (Side-Side-Side). The AA (Angle-Angle) Theorem states that two triangles with two congruent, corresponding angles are similar NOT necessarily congruent.
Three of these theorems do prove triangles to be congruent; SAS (Side-Angle-Side), ASA (Angle-Side-Angle), and SSS (Side-Side-Side). The AA (Angle-Angle) Theorem states that two triangles with two congruent, corresponding angles are similar NOT necessarily congruent.
Compare your answer with the correct one above
Which of the following theorems is used only to prove the congruence of two right triangles?
Which of the following theorems is used only to prove the congruence of two right triangles?
While all of these theorems can prove two triangles to be congruent the Hypotenuse-Leg Theorem (HL) is the only theorem out of these that can only prove two right triangles to be congruent. This theorem states that if two right triangles have one congruent leg and a congruent hypotenuse then they are congruent.
While all of these theorems can prove two triangles to be congruent the Hypotenuse-Leg Theorem (HL) is the only theorem out of these that can only prove two right triangles to be congruent. This theorem states that if two right triangles have one congruent leg and a congruent hypotenuse then they are congruent.
Compare your answer with the correct one above
Fill in the blanks below to complete the proof for the HL Theorem. Use the figure below to find the given information.
Fill in the blanks below to complete the proof for the HL Theorem. Use the figure below to find the given information.
Follow the detailed proof below.
Follow the detailed proof below.
Compare your answer with the correct one above
Prove that if one side of a triangle is longer than another side of the same triangle, then the angle opposite the longer side will be greater than the angle opposite the shorter side. Use the information that 
for triangle 
.
Prove that if one side of a triangle is longer than another side of the same triangle, then the angle opposite the longer side will be greater than the angle opposite the shorter side. Use the information that 
Follow the detailed proof below.
Follow the detailed proof below.
Compare your answer with the correct one above
What is the first step to any proof?
What is the first step to any proof?
In order to prove anything, we must first state the given information. This will allow us to move forward with the proof and make different connections based on the given information.
In order to prove anything, we must first state the given information. This will allow us to move forward with the proof and make different connections based on the given information.
Compare your answer with the correct one above
Which of the following is the altitude rule?
Which of the following is the altitude rule?
This can be represented by the following equation
This can be represented by the following equation
Compare your answer with the correct one above
True or False: The Base Angles Converse states that if two base angles are congruent, then their opposite sides are congruent.
True or False: The Base Angles Converse states that if two base angles are congruent, then their opposite sides are congruent.
Since the Base Angles Theorem states that if two adjacent sides are congruent then their opposite angles are congruent, then its converse assumes that the two base angles are congruent and then their opposite sides are congruent.
Since the Base Angles Theorem states that if two adjacent sides are congruent then their opposite angles are congruent, then its converse assumes that the two base angles are congruent and then their opposite sides are congruent.
Compare your answer with the correct one above
Consider the following theorem: If two triangles have two pairs of congruent corresponding sides and their included angle is congruent, then these two triangles are congruent. When proving this theorem, what information do we assume to begin the proof?
Consider the following theorem: If two triangles have two pairs of congruent corresponding sides and their included angle is congruent, then these two triangles are congruent. When proving this theorem, what information do we assume to begin the proof?
When theorems are presented to you in an “if-then” format, you always assume the entire “if” part. This allows you to construct an argument that you will be able to prove to be true using the given information.
When theorems are presented to you in an “if-then” format, you always assume the entire “if” part. This allows you to construct an argument that you will be able to prove to be true using the given information.
Compare your answer with the correct one above
Are the two triangles shown congruent?
Are the two triangles shown congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are equal and the correspond side is also equal therefore, the triangles are congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are equal and the correspond side is also equal therefore, the triangles are congruent.
Compare your answer with the correct one above
Are the two triangles congruent?
Are the two triangles congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
Compare your answer with the correct one above
Are the two triangles congruent?
Are the two triangles congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
Compare your answer with the correct one above
Are the two triangles congruent?
Are the two triangles congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are equal therefore, the triangles are congruent.
Compare your answer with the correct one above
Are the two triangles shown congruent?
Are the two triangles shown congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal and the correspond side is also not equal therefore, the triangles are not congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal and the correspond side is also not equal therefore, the triangles are not congruent.
Compare your answer with the correct one above
Are the two triangles shown congruent?
Are the two triangles shown congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal therefore, the triangles are not congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal therefore, the triangles are not congruent.
Compare your answer with the correct one above
Are the two triangles congruent?
Are the two triangles congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are not equal therefore, the triangles are not congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have all three sides defined, the Side, Side, Side geometric theorem can be used.
Looking at the triangles the corresponding sides are not equal therefore, the triangles are not congruent.
Compare your answer with the correct one above
Are the two triangles shown congruent?
Are the two triangles shown congruent?
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal therefore, the triangles are not congruent.
For two triangles to be congruent they must have equal corresponding angles and sides. There are five geometric theorems that can be used to prove whether triangles are congruent or not. Since, these two triangles have two defined angles and the side between the angles are defined as well, the Angle, Side, Angle geometric theorem can be used.
Looking at the triangles the corresponding angles are not equal therefore, the triangles are not congruent.
Compare your answer with the correct one above