1. 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angles of triangles, about the angles created when parallel lines are cut by a transversal and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and gives an argument in terms of transversals why this is so.

2. Describe two ways you can show that angle 2 is congruent to angle 7.
Angle 2 is vertical to angle 3 and 3 is corresponding to angle 7, so angle 2 is congruent to angle 7
Angle 2 is alternate exterior to angle 7.

3. If the measure of angle 1 is 140°, determine the measure of the remaining 7 angles. Find all the ways to justify each answer.
Angles 1, 4, 5 and 8 are 140°. Angles 2, 3, 6 and 7 are 40°. Vertical angles are 1 and 4, 2 and 3, 5 and 8, 6 and 7. Supplementary angles are 1 and 2, 2 and 4, 3 and 4, 1 and 3, 5 and 6, 6 and 8, 7 and 8, 5 and 7. Corresponding angles are 1 and 5, 2 and 5, 3 and 7, 4 and 8. Alternate exterior angles are 1 and 8, 2 and 7. Alternate interior angles are 3 and 6, 4 and 5.

4. Classify the triangle according to side length and angle measures.
The triangle is a right, isosceles triangle. It has one right angle. An exterior angle of 135° means the interior angle is 45°. This means the other angle is 45°.

5. The ratio of the interior angle measures of a triangle is 1:2:3
The ratio of the interior angle measures of a triangle is 1:2:3. What are the angle measures?
1x + 2x + 3x = x = 30°
The three angles are 30, 60, 90.

6. Are the triangles similar?
Yes. Based on the angle-angle criterion, the triangles are similar. The triangles both have angles of 55° and 61°.

7. There are two right angles
There are two right angles. In both triangles, one angle is twice the measure of another angle. Are the angles similar?
Maybe. If the 90° angle is is twice another, then the other two angles are each 45°. If the middle angle is twice the other, then the angles in the triangle are 90°, 60°, 30°.

8. Are the two triangles similar?
No, the angles in the yellow triangle are 90°, 46° and 44°. The angles in the red triangle are 56°, 90° and 34°.