### All Intermediate Geometry Resources

## Example Questions

### Example Question #1 : How To Find If Acute / Obtuse Triangles Are Congruent

Given: and .

True or false: It follows from the given information that .

**Possible Answers:**

False

True

**Correct answer:**

False

Examine the diagram below.

, , and , but . As a result, it is not true that . Therefore, the statement is false.

### Example Question #2 : How To Find If Acute / Obtuse Triangles Are Congruent

Given: and .

True or false: It follows from the information given that .

**Possible Answers:**

False

True

**Correct answer:**

False

The congruence of corresponding angles of two triangles does not alone prove that the triangles are congruent. For example, see the figures below:

The three angle congruence statements are true, but the sides are not congruent, so the triangles are not congruent. The statement is false.

### Example Question #3 : How To Find If Acute / Obtuse Triangles Are Congruent

Given: and .

True or false: It follows from the given information that .

**Possible Answers:**

False

True

**Correct answer:**

True

As we are establishing whether or not , then , , and correspond respectively to , , and .

By the Side-Side-Side Congruence Postulate (SSS), if all three pairs of corresponding sides of two triangles are congruent, then the triangles themselves are congruent. Between and , and are corresponding sides, their congruence is given. The other two congruences between corresponding sides are given, so the conditions of SSS are satisfied. is indeed true.

### Example Question #4 : How To Find If Acute / Obtuse Triangles Are Congruent

Given: and .

True or false: It follows from the given information that .

**Possible Answers:**

False

True

**Correct answer:**

False

As we are establishing whether or not , then , , and correspond respectively to , , and .

By the Side-Side-Side Congruence Postulate (SSS), if all three pairs of corresponding sides of two triangles are congruent, then the triangles themselves are congruent. However, if we restate the first side congruence as

and examine it with the other two:

We see that while we can invoke SSS, the points correspond to , respectively. The triangle congruence that follows is therefore .

The answer is therefore false.

### Example Question #5 : How To Find If Acute / Obtuse Triangles Are Congruent

Given: and .

True or false: It follows from the given information that .

**Possible Answers:**

True

False

**Correct answer:**

True

As we are establishing whether or not , then , , and correspond respectively to , , and .

By the Side-Angle-Side Congruence Postulate (SAS), if two pairs of corresponding sides and the included angle of one triangle are congruent to the corresponding parts of a second, the triangles are congruent. and , indicating congruence between corresponding sides, and , indicating congruence between corresponding included angles. This satisfies the conditions of SAS, so is true.

### Example Question #6 : How To Find If Acute / Obtuse Triangles Are Congruent

Refer to the above two triangles. By what statement does it follow that ?

**Possible Answers:**

The Angle-Angle-Side Theorem

The Hinge Theorem

The Angle-Side-Angle Postulate

The Converse of the Pythagorean Theorem

The Converse of the Isosceles Triangle Theorem

**Correct answer:**

The Angle-Angle-Side Theorem

We are given that two angles of - and - and a nonincluded side are congruent to their corresponding parts, , , and of . It follows from the** Angle-Angle-Side Theorem** that .

### Example Question #7 : How To Find If Acute / Obtuse Triangles Are Congruent

Refer to the above two triangles. By what statement does it follow that ?

**Possible Answers:**

The Angle-Angle Postulate

The Triangle Midsegment Theorem

The Hinge Theorem

The Isosceles Triangle Theorem

The Side-Angle-Side Postulate

**Correct answer:**

The Side-Angle-Side Postulate

We are given that two sides of - sides and - and their included angle are congruent to their corresponding parts, sides and and of . It follows from the **Side-Angle-Side Postulate** that .