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

Study concepts, example questions & explanations for Intermediate Geometry

varsity tutors app store varsity tutors android store

Example Questions

Example Question #48 : Triangles


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

Possible Answers:

The Hinge Theorem

The Converse of the Isosceles Triangle Theorem

The Side-Angle-Side Postulate

The Isosceles Triangle Theorem

The Side-Side-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 #49 : Triangles

Given:  and  such that 

Which statement(s) must be true?



Possible Answers:

(b) but not (a)

(a) and (b)

(a) but not (b)

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.

Learning Tools by Varsity Tutors