Download CH 4 Review Advanced Geometry Classify each triangle as acute

NAME
DATE
CH 4 Review
4
PERIOD
SCORE
Advanced Geometry
Classify each triangle as acute, equiangular, obtuse, or right.
85°
100°
30°
40°
40°
90°
65°
60°
30°
Classify each triangle in the figure at the right by its angles and sides.
B
4. △
5. △
6. △
7. △
E
A
D
C
ALGEBRA Draw a picture of each triangle. For each triangle, find x and the measure of each side.
8. △FGH is an equilateral triangle with FG = x + 5, GH = 3x – 9, and FH = 2x – 2.
9. △LMN is an isosceles triangle, with LM = LN, LM = 3x – 2, LN = 2x + 1, and MN = 5x – 2.
Find the measures of the sides of △KPL and classify each triangle by its sides.
10. (–
2), P(2, 1), (–
Chapter 4
–
8
Geometry
Find each measure.
14.
11.
3
12.
15.
2
1
1
16.
13.
4
2
17.
3
18.
E
3
2
19. Given: 𝐷𝐸 ∥ 𝐵𝐶
∠1 ≅ ∠2
C
A
1
D
4
Prove: 𝐴𝐵 ≅ 𝐴𝐶
2 47
Use the picture at the right to determine which of the three
given angle s is the largest.
20. ∡3, ∡5, ∡4
1
21. ∡3, ∡1, ∡2
3
22. ∡1, ∡7, ∡8
List the angles and sides of each triangle in order from smallest to largest.
23. R
24. K
6
M
24°
2
P
Q
5
5 6
98°
L
8 9
5
Use your geometer to draw the following triangles, and then find the altitude from the vertex.
25. Isosceles 𝛥ABC with vertex B, legs 10
inches, and base 12 inches.
26. Isosceles 𝛥XYZ with vertex X, legs 11
inches, and base 8 inches.
27. Equilateral 𝛥MON with sides 14 inches.
29. a. Graph 𝛥ABC at the right where A(-7, 7), B(3, 5), and
C(-2, -4).
b. Find the coordinates of median 𝑀𝐶 .
c. Write the equation of the line that contains median 𝑀𝐵.
28. Isosceles 𝛥EFG with vertex G, legs 17
inches, and base 16 inches.
Determine if the following side lengths can make a triangle. Explain with algebra.
30. 7, 4, 2
31. 5, 12, 13
32. 6, 6, 20
33. 13, 10, 8
Find the area of the following triangles.
34.
35.
14
8 2
14
8
10
8
36. a. Graph 𝛥ABC at the right where A(-8, 2), B(-5, 8), and
C(3,0).
b. Write the equation of the line that contains altitude 𝐷𝐶 .
37. Triangle ABC has vertices A(0, 4), B(1, 2), and C(4, 6). Determine whether triangle ABC is a right
triangle. Explain.