All SSAT Upper Level Math Resources
Example Questions
Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar
;
;
has perimeter 400.
Which of the following is equal to ?
The perimeter of is actually irrelevant to this problem. Corresponding sides of similar triangles are in proportion, so use this to calculate
, or
:
Example Question #2 : How To Find If Two Acute / Obtuse Triangles Are Similar
;
;
has perimeter 300.
Evaluate .
Insufficient information is given to answer the problem.
The ratio of the perimeters of two similar triangles is equal to the ratio of the lengths of a pair of corresponding sides. Therefore,
and
, or
By one of the properties of proportions, it follows that
The perimeter of is
, so
Example Question #3 : How To Find If Two Acute / Obtuse Triangles Are Similar
;
;
;
has perimeter 90.
Give the perimeter of .
The ratio of the perimeters of two similar triangles is the same as the ratio of the lengths of a pair of corresponding sides. Therefore,
Example Question #4 : How To Find If Two Acute / Obtuse Triangles Are Similar
.
Evaluate .
These triangles cannot exist.
The similarity of the triangles is actually extraneous information here. The sum of the measures of a triangle is , so:
Example Question #1 : How To Find If Two Acute / Obtuse Triangles Are Similar
Given: and
;
and
.
Which of the following statements would not be enough, along with what is given, to prove that ?
The given information is enough to prove the triangles similar.
The given information is enough to prove the triangles similar.
Two pairs of corresponding angles are stated to be congruent in the main body of the problem; it follows from the Angle-Angle Similarity Postulate that the triangles are similar. No further information is needed.
Example Question #6 : How To Find If Two Acute / Obtuse Triangles Are Similar
.
. Which of the following is the ratio of the area of
to that of
?
The similarity ratio of to
is equal to the ratio of two corresponding sidelengths, which is given as
; the similarity ratio of
to
is the reciprocal of this, or
.
The ratio of the area of a figure to that of one to which it is similar is the square of the similarity ratio, so the ratio of the area of to that of
is
Example Question #131 : Properties Of Triangles
;
Which of the following is true about ?
is isosceles and acute.
is isosceles and obtuse.
is scalene and acute.
is scalene and obtuse.
None of the other responses is correct.
is scalene and obtuse.
Corresponding angles of similar triangles are congruent, so the measures of the angles of are equal to those of
.
Two of the angles of have measures
and
; its third angle measures
.
One of the angles having measure greater than makes
- and, consequently,
- an obtuse triangle. Also, the three angles have different measures, so the sides do as well, making
scalene.
Example Question #8 : How To Find If Two Acute / Obtuse Triangles Are Similar
;
;
.
Which of the following correctly gives the relationship of the angles of ?
Corresponding angles of similar triangles are congruent, so .
Consequently,
Therefore,
.
Example Question #9 : How To Find If Two Acute / Obtuse Triangles Are Similar
;
.
Which of the following correctly gives the relationship of the angles of ?
Corresponding sides of similar triangles are in proportion; since ,
Therefore, .
The angle opposite the longest (shortest) side of a triangle is the angle of greatest (least) measure, so
.
Example Question #10 : How To Find If Two Acute / Obtuse Triangles Are Similar
.
Order the triangles by perimeter, least to greatest.
and
are corresponding sides of their respective triangles, and
, so it easily follows from proportionality that each side of
is shorter than its corresponding side in
. Therefore,
is of lesser perimeter than
. By the same reasoning, since
,
is of lesser perimeter than
.
The correct response is
All SSAT Upper Level Math Resources
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