1. 5.4(b) Notes: Proving Congruent and Right Angles
Date:
5.4(b) Notes: Proving Congruent and Right Angles
Lesson Objective: Write proofs involving congruent and right angles.
CCSS: G.CO.9 Prove theorems about lines and angles.

2. Lesson 1: Complement Theorem
Draw a right angle. What is the measure of a right angle? ____

3. Lesson 1: Complement Theorem
Draw / 1 with the measure of 60°. What is the measure of / 2? ____ 1
60° 2

4. Complement Theorem:
If the noncommon sides of 2 adjacent / s form a right / , then the / s are complementary / s.
Example: m/ 1 + m/ 2 = 90° 1 2

5. Lesson 2: Using the Complement Theorem
Prove that m/ 3 is 49° if m/ 2 = (2x + 7)° and m/ 3 = (3x – 2)°.

6. Lesson 3: Vertical Angles
Draw vertical angles using one red line and one blue line each approximately 3” long. Number the angles with the numbers spaced out as shown. 1 3

7. Lesson 3: Vertical Angles
Trace the diagram onto tissue paper, using the same colors, but writing the numbers closer to the center. 1 3

8. Lesson 3: Vertical Angles
Rotate the tissue paper around and match the lines. Tape it on top of the first diagram. What do you notice? 1 3

9. Vertical Angles Theorem:
If 2 angles are vertical, then they are congru-ent. (Vert. / s )
Example: / / 3 and / / 4 1 3

10. Lesson 4: Using Vertical Angles
If / 2 and / 4 are vertical angles, m/ 2 = 6x + 2 and m/ 4 = 8x – 14, find m/ 2 and m/ 4. 1 3

12. 5.4: Do I Get It? Yes or No
Find m/ 1 if m/ 2 = 56° and m/ JKL = 145°.

13. 5.4: Do I Get It? Continued
2. Using a transit, a surveyor sights the top of a hill and records an angle measuring about 73°. What is the measure of the angle the top of the hill makes with the horizon? Justify each step.

14. 5.4: Do I Get It? Continued
3. Ray DB bisects / ADC. Find m/ 2 if m/ 3 = 55°.