# Lesson 10 Centers of a Triangle Practice Understanding

Figure 1 has been rotated

### 1.

Use Figure 3 to explain how you know the exterior angle

### 2.

Use Figure 3 to explain how you know the sum of the angles in a triangle is always

### 3.

Use Figure 2 to explain how you know the sum of the angles in a quadrilateral is always

### 4.

Use Figure 2 to explain how you know the opposite angles in a parallelogram are congruent.

### 5.

Use Figure 2 to explain how you know the opposite sides in a parallelogram are parallel and congruent.

### 6.

Use Figure 2 to explain how you know when two parallel lines are crossed by a transversal, the alternate interior angles are congruent.

### 7.

Use Figure 2 and/or 3 to explain how you know when two parallel lines are crossed by a transversal, the same-side interior angles are supplementary.

Use the diagram for problems 8–10.

### 8.

Prove that

Write a two-column proof.

### 9.

Prove that

Given

### 10.

Prove that

### 11.

Construct the inscribed circle for the triangle.

### 12.

Construct the circumscribed circle for the triangle.

### 13.

Why is the intersection of the perpendicular bisectors of the three sides of a triangle the circumcenter of the triangle? In other words, why is the point of intersection of these segments the center of the circle that circumscribes the triangle? Construct the perpendicular bisector for the segment

Use what you know about triangles and parallelograms to find each measure.