1. 4-2 Vocabulary Auxiliary line Corollary Interior Exterior
Interior angle
Exterior angle
Remote interior angle

2. 4.2 Angle Relationships in Triangles
Geometry

3. Thm 4-2-1 Triangle Sum Theorem
The sum of angle measures of a triangle is 180°. m∠A + m∠B + m∠C = 180° B
A C

4. Ex. 1
1a.)Find the
1b.) Find the Y
62° °
W X Z
12°

5. Corollary – a theorem whose proof follows directly from another theorem.
(2 corollaries to the Triangle Sum Theorem.)
Corollary The acute angles of a right triangle are complementary.
Corollary The measure of each angle of an equiangular triangle is 60°.

6. Ex. 2
One of the acute angles in a right triangle measures 2x°. What is the measure of the other acute angle?

7. Thm 4-2-4 Exterior Angle Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of its remote interior angles.
m∠4 = m∠1 + m∠2 1 2 4 3

8. Ex. 3
Find the
(5x-60)°
A C D
(2x+3)°

9. 4-2-5 Thm 3rd angles Thm
If 2 s of one Δ are  to 2 s of another Δ, then the 3rd pr. s are also .

10. Ex. 4 Find m∠K and m∠J K ))
(4y²)° J
(6y² - 40 )° )) ) H F ) )) G I

11. Ex 5: find x ) )
22o
X = 14 ))
87o ))
(4x+15)o

12. If Δ ABC is  to Δ XYZ, which angle is  to C?

13. Prove Corollary 4-2-3 using 2 column proofs
Ex. 6
Given: Δ ABC is equiangular.
Prove: mA = m B = m C = 60°

14. Assignment

15. Congruent Figures ( )))) ))) (( ( )))) ))) (( B A ___
2 figures are congruent if they have the exact same size and shape.
When 2 figures are congruent the corresponding parts are congruent. (angles and sides)
Quad ABDC is congruent to Quad EFHG
___
___
))))
)))
___ (( D C F ( E
___
___
___
))))
___
))) (( H G

16. Ex 6: ABCD is  to HGFE, find x and y.
9cm A B E
91o F
(5y-12)o
86o
113o D C H G
4x-3cm
X = 3, y = 25

17. Thm 4.4 Props. of  Δs A
Reflexive prop of Δ  - Every Δ is  to itself (ΔABC  ΔABC).
Symmetric prop of Δ  - If ΔABC  ΔPQR, then ΔPQR  ΔABC.
Transitive prop of Δ  - If ΔABC  ΔPQR & ΔPQR  ΔXYZ, then ΔABC  ΔXYZ. B C P Q R X Y Z

18. Given: seg RP  seg MN, seg PQ  seg NQ , seg RQ  seg MQ, mP=92o and mN is 92o. Prove: ΔRQP  ΔMQN N R
92o Q
92o P M

19. Statements Reasons 1. 1. given 2. mP=mN 2. subst. prop =
3. P  N def of  s
4. RQP  MQN vert s thm
5. R  M rd s thm
6. ΔRQP  Δ MQN def of  Δs