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Example Questions
Example Question #48 : Triangles
Refer to the above diagram. and
. By what statement does it follow that
?
The Hinge Theorem
The Converse of the Isosceles Triangle Theorem
The Side-Angle-Side Postulate
The Isosceles Triangle Theorem
The Side-Side-Side Postulate
The Side-Side-Side Postulate
In addition to the fact that and
, we also have that
, since, by the Reflexive Property of Congruence, any segment is congruent to itself. We can restate this in a more usable form as
; since we have three side congruences between triangles, it follows from the Side-Side-Side Postulate that
.
Example Question #49 : Triangles
Given: and
such that
Which statement(s) must be true?
(a)
(b)
(b) but not (a)
(a) and (b)
(a) but not (b)
Neither (a) nor (b)
Neither (a) nor (b)
Neither similarity nor congruence of the two triangles follows from the statements given, as can be seen from the figure below:
,
, and
. However, the triangles are not similar, as
and
, so at least one pair of corresponding sides is not in proportion. Therefore,
The triangles are not similar, and thus cannot be congruent either, so neither statement holds.
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