### All Intermediate Geometry Resources

## Example Questions

### Example Question #41 : Acute / Obtuse Isosceles Triangles

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

**Possible Answers:**

The Converse of the Isosceles Triangle Theorem

The Side-Side-Side Postulate

The Hinge Theorem

The Isosceles Triangle Theorem

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 #1 : How To Find If Of Acute / Obtuse Isosceles Triangles Are Congruent

Given: and such that

Which statement(s) *must* be true?

(a)

(b)

**Possible Answers:**

(a) and (b)

Neither (a) nor (b)

(b) but not (a)

(a) but not (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:

, , 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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