1. Warm Up
5 minutes c d
List 2 pairs of…
A. Vertical Angles
B. Linear Pair
C. Alternate Interior
D. Alternate Exterior
E. Corresponding Angles
F. Consecutive Interior 8 7 9 5 6 a 10 4 3 2 1 14 13 b 11 12

2. Triangle Sum Theorem
Mr. Riddle

3. Classifying Triangles by Angles
Acute – 3 acute angles
Right – 1 right angle
Obtuse – 1 obtuse angle
Equiangular – 3 congruent angles

4. Class Activity
You will have 30 minutes to complete the “Discovering the Triangle Sum Theorem”

5. Triangle Sum Theorem: Wrap-Up
What did we discover?

6. Practice: 𝒎∠𝑻=𝟕𝟏 𝒎∠𝑫=𝟒𝟗 𝒙=𝟏𝟐 𝒎∠𝑪=𝟔𝟓 12.) 𝑚∠𝐴+𝑚∠𝑀+𝑚∠𝑇=180 27+82+𝑚∠𝑇=180
109+𝑚∠𝑇=180
𝒎∠𝑻=𝟕𝟏
13.) 𝑚∠𝐷+𝑚∠𝑂+𝑚∠𝐺=180
𝑚∠𝐷+41+90=180
𝑚∠𝐷+131=180
𝒎∠𝑫=𝟒𝟗
14.) 𝑚∠𝐴+𝑚∠𝐵+ 𝑚∠𝐶=180
2𝑥 𝑥+5 =180
7𝑥+96=180
7𝑥=84
𝒙=𝟏𝟐
𝑚∠𝐴=2𝑥+1
𝑚∠𝐴=
𝒎∠𝑨=𝟐𝟓
𝑚∠𝐶=5𝑥+5
𝑚∠𝐶=
𝒎∠𝑪=𝟔𝟓

7. Challenge Problem
Find the measure of each missing angle. Explain how you found each angle.
𝒎∠𝟏=𝟏𝟐𝟑
𝒎∠𝟐=𝟓𝟐
𝒎∠𝟑=𝟐𝟗
𝒎∠𝟒=𝟓𝟔
𝒎∠𝟓=𝟓𝟕
𝒎∠𝟔=𝟏𝟐𝟑
𝒎∠𝟕=𝟓𝟕
𝒎∠𝟖=𝟐𝟖.𝟓
𝒎∠𝟗=𝟐𝟖.𝟓

8. Exterior Angles Theorem
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STUDENT:
𝑚∠1=
𝑚∠2=
𝑚∠3=
𝑚∠4= 1 2 3 4
1.) Do you notice any pattern between angles 1, 2, and 4?
2.) Can you create a theorem that has to do with the exterior angle of a triangle?
Hint: Start your theorem, “The exterior angle of a triangle is equal to…”

9. Exterior Angle Theorem
Exterior angle equals the sum of the two remote interior angles. A B C 1 2 3 4

10. Congruent Figures
Congruent Figures – two figures are congruent if they have the same shape and same size
Two figures are congruent if they can be obtained from the other by rigid motions. (a sequence of reflections, rotations, and/or translations)
Since ∆𝐷𝐸𝐹 is a rotation of ∆𝐴𝐵𝐶 and a rotation is a rigid motion, ∆𝐴𝐵𝐶≅∆𝐷𝐹𝐸. D E F A B C

11. Example 1: Triangle Congruence Statement
If two triangles are congruent, then all 3 sides of one triangle are congruent to all 3 sides of the other.
Also all 3 angles of one triangle are congruent to and all 3 angles of the other triangle.
To indicate that two triangles are congruent, we must write a triangle congruent. D E F A B C
In the diagram, ∆𝐴𝐵𝐶≅∆𝐷𝐹𝐸.
∠𝐴≅∠𝐷
∠𝐵≅∠𝐹
∠𝐶≅∠𝐸
𝐴𝐵 ≅ 𝐷𝐹
𝐵𝐶 ≅ 𝐹𝐸
𝐴𝐶 ≅ 𝐷𝐸

12. Problem #1 Label the congruent parts of the triangles.
Congruent Angles:
Congruent Sides:
Triangle Congruence Statement: ∆𝑋𝑌𝑍≅∆𝑆𝑅𝑇 Y X Z R S T

13. Example #2: Finding the Missing Measures of Congruent Figures
In the diagram, ∆𝐽𝐾𝐿≅∆𝑀𝑁𝑂. Find the value of the missing variables.
Since 𝑀𝑁 ≅ 𝐽𝐾
To solve for y:
𝑥−2𝑦=8
30 −2𝑦=8
−2𝑦=−22
𝑦=11
Since ∠𝐽≅∠𝑀:
To solve for x:
3𝑥=90
𝑥=30
Since ∠𝐿≅∠𝑂
To solve for z:
2𝑧=40
z=20 M N O
3𝑥°
𝑥−2𝑦 𝑖𝑛. J K L
8 𝑖𝑛.
2z°
40°

14. REMEMBER!
The congruent parts of the triangles must match up with the corresponding parts in each triangle!!!

15. Problem #2 In the diagram 𝐷𝐸𝐹𝐺≅𝑆𝑃𝑄𝑅. x = 8 y = 10
a. Find the value of x.
b. Find the value of y.
x = 8
y = 10 D E F G
8 ft
12 ft P S R Q
(2𝑥−4) ft