Honors Geometry Midterm Review
Part 1 - Always (A), Sometimes (S), Never (N)
1) The supplement of an acute angle is an obtuse angle.
2) If is the perpendicular bisector of , then is the perpendicular bisector of .
3) Two lines perpendicular to the same line are perpendicular to each other.
4) The bisector of an angle of a triangle bisects the side opposite the angle.
5) If two triangles have all their corresponding angles congruent, then their corresponding sides are congruent.
6) If the m∠X < m∠Y, then the supplement of ∠X is greater than the supplement of ∠Y.
Part 2 – Multiple Choice
1) Which of the following may be assumed from the diagram?
- ∠WXY is a right angle
- Z is the midpoint of
- ∠WZX is a right angle
- ∠Y is acute
- None of these
2) Which of the following is false?
- All of these
3) If ∠1 is supplementary to ∠2, ∠3 is supplementary to ∠4, and ∠2 = ∠4, then:
a. ∠1 ∠3
b. ∠1 ∠2
c. ∠1 ∠4
d. ∠1 is supplementary to ∠3
e. ∠2 is supplementary to ∠4
4) In the diagram, and ∠A ∠D. In order to conclude that rABC rDEF by ASA, it is necessary to know that:
a. ∠B ∠E
b. ∠ACB ∠DEF
c. ∠ABC ∠DFE
d. ∠ABC ∠DFB
e. ∠DFB ∠ACE
5) If the measure of an angle exceeds its supplement by 20o, then the measure of the angle is:
a. 100o
b. 80o
c. 55o
d. 35o
e. 125o
6) In order to prove that a point lies on the perpendicular bisector of a segment, it is necessary to show:
a. The point is on the segment
b. The distance from the point to the endpoints of a segment is equal
c. The point is the midpoint of the segment
d. The point is the perpendicular bisector of the segment
e. All of the above
7) If two angles are congruent and supplementary then the angles must be:
a. Adjacent angles
b. Acute angles
c. Obtuse angles
d. Straight angles
e. Right angles
8) If the vertex angle of an isosceles triangle is 40o, then each of the base angles is:
a. 70o
b. 140o
c. 40o
d. 20o
e. 50o
9) Given the diagram as marked with , then ∠AFE equals:
a. 162o
b. 164o
c. 18o
d. 16o
e. 57 1/7o
10) If the angles of a triangle are xo, yo, and (xo + yo), the triangle must be a(n):
a. Isosceles triangle b. Equilateral triangle
c. Obtuse Triangle d. Right triangle
e. Acute triangle
11) Given the diagram as marked, find m∠ACB.
a. 23o
b. 102o
c. 42o
d. 78o
e. none of these
12) Which of the following is not a correct method of proving congruent triangles:
a. SAS
b. ASA
c. SSA
d. SSS
e. HL
13) In the diagram below, which of the following is not always true:
a. b + c + d = 180o
b. c = d
c. a = b + c
d. a + d = 180o
e. all are always true
Part 3 – Matching
Part 5 - Proofs
Given:
Prove:
Given:
Prove:
and
Given: ∠ABE≅ ∠AEB
Prove:
Given: r
D and E trisect BC
∠1≅ ∠2
Prove: ∠3≅ ∠4
Part 4 – Algebra Practice
In Exercises 1, point M is between L and N on LN. Use the given information to write an equation in terms of x. Solve the equation (disregard any answers that do not make sense in the context of the problem). Then find LM and MN.
1. LM = x2
MN = x
LN = 56
Find the values of x-and y.
2. 3.
4. 5.
Tell whether the lines through the given points are parallel, perpendicular, or neither.
6. Line 1: (–5, 6), (–2, 2)
Line 2: (4, 2), (7, 6)
7. Line 1: (–4, 8), (6, 2)
Line 2: (–4, 1), (–1, 6)
8. Line 1: (–7, –4), (5, 7)
Line 2: (2, 3), (14, 14)
9. Line 1: (–5, –3), (6, 3)
Line 2: (1, 9), (7, –2)
Find the coordinates of the midpoint of the segment with the given endpoints.
10. S (4, –1) and T (6, 0)
11. L (4,2) and P (0, 2)
The endpoints of two segments are given. Find each segment length.
Tell whether the segments are congruent.
12. A (2, 6), B (0, 3)
C (–1, 0), D (1, 3)
Find the values of x and y.
13. 14.
Find the values of x and y.
15. 16.
17. Find the values of x, y, and z 18. Find the perimeter of the triangle.
Find the values of x and y, if possible. If not possible, explain your reasoning.
19. 20.
21. An image and its translation are given. 22. Solve for x:
Sketch the original figure:
23.
24. Point L is the centroid of DNOM. Use the given information to find the value of x.
a. OL = 8x and OQ = 9x + 6
b. NL = x + 4 and NP = 3x + 3
c. ML = l0x – 4 and MR = 12x + 18
24. A logo to be placed on the cabin is being designed using the triangles to the right. Are the triangles congruent? Construct a mathematical argument to justify your answer.
______
b. Mrs. Dias decided to connect points A and D to create a different design. What is the best classification for the new triangle created - ΔABD? How do you know?
______