1. Geometry--Ch. 4 Review Obtuse Scalene
1) Classify the triangle according to its angles and its sides:
61o
25o
94o
The missing angle is 94o, so the triangle is OBTUSE.
Since the angles are all different, so are the sides. This makes the triangle SCALENE.
Obtuse Scalene

2. Geometry--Ch. 4 Review Acute Isosceles
2) Classify the triangle according to its angles and its sides:
74o
32o
74o
The missing angle is 74o.
Acute Isosceles

3. Geometry--Ch. 4 Review
3) Given: DJKL ≅ DRST. Find the value of x and y: J K L
(9x-2)o
36o R S T
70o
36o
(7y+11)o
9x – 2 = 70
180 – 70 – 36 = 74
9x = 72
7y = 74
7y = 63
x = 8
y = 9

4. Geometry--Ch. 4 Review
4) The angles of a triangle are in the extended ratio :21:22. Find the measure of each angle:
You can picture the triangle to look like this
17x
21x
22x
17x + 21x + 22x = 180
60x = 180
x = 3
The angle measures are…
17(3)
21(3)
22(3)
51o
63o
66o

5. Geometry--Ch. 4 Review
5) Solve for x, then calculate the measure of the exterior angle:
2x+18
6x-3
3x-4
(2x+18) + (3x-4) = 6x-3
5x+14 = 6x-3
14 = x-3
x = 17

6. NO Geometry--Ch. 4 Review
6) Determine if you can prove whether the following triangles are congruent (yes or no). If yes, state the theorem or postulate you used: NO

7. Yes; HL Geometry--Ch. 4 Review
7) Determine if you can prove whether the following triangles are congruent (yes or no). If yes, state the theorem or postulate you used:
Yes; HL

8. Yes; SSS Geometry--Ch. 4 Review
8) Determine if you can prove whether the following triangles are congruent (yes or no). If yes, state the theorem or postulate you used:
Yes; SSS

9. These two angles are also ≅ due to the Isosceles Triangle Theorem.
Geometry--Ch. 4 Review
38o x
9) Find the value of x:
These two angles are ≅ due to the Isosceles Triangle Theorem. x
Since all triangles are 180o, the two missing angles are both 71o.
Since vertical angles are =, this angle is also 71o.
These two angles are also ≅ due to the Isosceles Triangle Theorem.
x + x = 180
2x = 109
2x = 180
x = 54.5

10. Geometry--Ch. 4 Review 10) Find the value of x:
Due to the Isosceles Triangle Theorem, we know that the base angles are ≅.
10x - 6
The angle sum in any triangle is 180o, so we have…
(10x – 6) + (10x – 6) + (22x + 3) = 180
42x - 9 = 180
42x = 189
x = 4.5

11. Alternate Interior ∠s are ≅
Geometry--Ch. 4 Review A B C D E
11) Given: AB ll CD, AE ≅ CE Prove: BE ≅ DE
Statements
Reasons
AB ll CD, AE ≅ CE
Given
∠BAE ≅ ∠DCE
Alternate Interior ∠s are ≅
Vertical ∠s are ≅
∠AEB ≅ ∠CED
ASA
DABE ≅ DCDE
CPCTC
BE ≅ DE

12. Geometry--Ch. 4 Review I E H F G
12) Given: ∠EIF ≅ ∠HIG, ∠E ≅ ∠H Prove: ∠IFG ≅ ∠IGF
Statements
Reasons
Given
∠EIF ≅ ∠HIG, ∠E ≅ ∠H
EI ≅ HI
Isos. D Thm Converse
DIFE ≅ DIGH
ASA
CPCTC
IF ≅ IG
Isosceles D Theorem
∠IFG ≅ ∠IGF