Download Honors Geometry Unit #2 Review Topics: • Points, lines, planes

Honors Geometry
Unit #2 Review
Topics:
 Points, lines, planes, collinear, coplanar, notation, midpoint formula
 Union and intersection
 Angles, notation, classification,
 Congruence
 Midpoints, bisectors, and trisectors
 Counterexamples
 Assumptions about diagrams
 Perpendicular, complementary, supplementary
 Vertical angles and the Vertical Angle Theorem (VAT)
 Algebra review of solving quadratic equations by factoring and solving systems of linear
equations
Review Problems:
1. Refer to the figure to the right.
a. Name three collinear points.
b. Name four coplanar points.
c. Name three noncollinear points.
d. Name four
noncoplanar points.
e. Find R  DF .
f. Find HI  JI .
 
g. Find CG  FG
h. Find P  R.
 
i. Find IL  LI .
H
E
A
P
F
I
L
D
A
J
R
G K
B
C
2. Graph A(-8,3), B(5,1), C(3,-6), and D(-2,-3).

a. Draw CA .
b. Find AD.
c. Find the midpoint of BC .
d. Find the slope of AD and the slope of BC . Are the segments parallel, perpendicular, or
neither?
e. Find and label a point F so that CF  BC .
f. Find and label a point G so that AGD is a straight angle.
3. If E is acute and mE = 6x + 15, find all possible values of x.
4. If PQR is a straight angle and mPQR = 3 x 2  6 x  108 , find all possible values of x.
5. In the diagram below, JK  ML . Is M a right angle? Give an explanation for your answer.
6x - 2
J
M 12x°
5x + 5
K
L

6. Draw
a
diagram
to
illustrate
the
problem,
then
give
an
answer:
ABC
is
trisected
by
BD and


BE . DBE is bisected by BX . If mABC = 81°, what is mDBX?
7. Two complementary angles are in a ratio of 7:8. Find the measure of the smaller angle.
8. One of two supplementary angles is 30 more than 5 times the other. What is the measure of the
larger angle?
9. If M is the midpoint of AB , AM 
2
x  58
, find BM.
x  1 and AB 
3
5
10. Find the measure of each numbered angle in the diagram below.
6
4
3
1 2
33°
5
11. In the diagram below, m1  5 x  2 y, m 2  6 x  10 y  7 , and m3  80  7 y . Are the lines
perpendicular? Show all of your work and give an explanation of your answer.
2
1
3
***Note: In addition to problems similar to the ones above there will be some True/False questions on
your test.
Unit #2 Review Key:


1. a. ex: H,I,J b. ex: A,E,F,D c. ex: H,I,L d. ex: H,I,L,E e. D f. HJ g. G h. AD i. IL
5
2. b. 6 2 c. (4,  ) d. 1 and 2/7; neither
2
3. -5/2 < x < 25/2
4. -6 and 4
5. Since x is 7, mM = 84°, so M is not a right angle.
6. 13.5°
7. 84°
8. 155°
9. 7
10. m1 = m2 = 90°; m3 = 147°; m4 = 33°; m5 = m6 = 147°
11. x = 15 and y = -1; m1 = 73° so the lines are not perpendicular.