Intermediate Geometry : How to find if of acute / obtuse isosceles triangles are congruent

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

Example Question #46 : Triangles


Refer to the above diagram.  and . By what statement does it follow that 

Possible Answers:

The Hinge Theorem

The Isosceles Triangle Theorem

The Converse of the Isosceles Triangle Theorem

The Side-Side-Side Postulate

The Side-Angle-Side Postulate

Correct answer:

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 #47 : Triangles

Given:  and  such that 

Which statement(s) must be true?



Possible Answers:

(a) and (b)

(a) but not (b)

(b) but not (a)

Neither (a) nor (b)

Correct answer:

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:

Isosceles 1

, and . However, the triangles are not similar, as 


, 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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