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

## Example Questions

### Example Question #48 : Acute / Obtuse Isosceles Triangles Refer to the above diagram. and . By what statement does it follow that The Converse of the Isosceles Triangle Theorem

The Hinge Theorem

The Side-Side-Side Postulate

The Side-Angle-Side Postulate

The Isosceles Triangle Theorem

The Side-Side-Side Postulate

Explanation:

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 : Acute / Obtuse Isosceles Triangles

Given: and such that   Which statement(s) must be true?

(a) (b) (a) but not (b)

(b) but not (a)

(a) and (b)

Neither (a) nor (b)

Neither (a) nor (b)

Explanation:

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. 