Download Name Date PD CP Geometry Chapter 3Review Given the following

Name
CP Geometry
Date
Chapter 3Review
PD
1.) Given the following conditional statement, write the inverse, converse and contrapositive. Is it
possible to write a TRUE biconditional? If so, write the biconditional. If not, explain why a true
biconditional cannot be written.
Conditional: If two angles are supplementary to the same angle, then the two angles are congruent.
Inverse:
Converse:
Contrapositive:
Biconditional:
2.) ∠𝟏 𝐚𝐧𝐝 ∠𝟐 𝐚𝐫𝐞 𝐯𝐞𝐫𝐭𝐢𝐜𝐚𝐥 𝐚𝐧𝐠𝐥𝐞𝐬. 𝒎∠𝟏 = 𝟑𝒙 − 𝟒 𝐚𝐧𝐝 𝒎∠𝟐 = 𝟐𝒙 + 𝟏.
𝐅𝐢𝐧𝐝 𝐭𝐡𝐞 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝒙 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐦𝐞𝐚𝐬𝐮𝐫𝐞 𝐨𝐟 𝐞𝐚𝐜𝐡 𝐚𝐧𝐠𝐥𝐞.
x=
m∠1 =
m∠2 =
3.) Find the midpoint of ̅̅̅̅
𝑹𝒁 given the points 𝐑(𝟓, −𝟖) 𝐚𝐧𝐝 𝐙(−𝟏, −𝟏𝟒).
4.) ∠𝟑 𝐚𝐧𝐝 ∠𝟒 𝐚𝐫𝐞 𝐚 𝐥𝐢𝐧𝐞𝐚𝐫 𝐩𝐚𝐢𝐫. 𝒎∠𝟑 = 𝟏𝟎(𝒙 + 𝟑) 𝐚𝐧𝐝 𝒎∠𝟒 = 𝟏𝟓𝒙.
𝐅𝐢𝐧𝐝 𝐭𝐡𝐞 𝐯𝐚𝐥𝐮𝐞 𝐨𝐟 𝒙 𝐚𝐧𝐝 𝐭𝐡𝐞 𝐦𝐞𝐚𝐬𝐮𝐫𝐞 𝐨𝐟 𝐞𝐚𝐜𝐡 𝐚𝐧𝐠𝐥𝐞.
x=
m∠3 =
In Exercises 5-8, use the diagram of a cube to the right.
5.) List 4 parallel lines.
6.) List 4 pairs of perpendicular lines.
7.) List 4 pairs of skew lines.
8.) List all parallel planes.
m∠4 =
9.)
List all corresponding angles.
10.)
List all consecutive interior angles.
11.)
List all alternate exterior angles.
12.)
List all alternate interior angles.
Find the value of x.
13.)
8
14.)
Given 𝒍 ||𝒎 𝐚𝐧𝐝 𝒎∠𝟒 = 𝟏𝟏𝟐°, 𝐟𝐢𝐧𝐝 𝐚𝐥𝐥 𝐭𝐡𝐞 𝐨𝐭𝐡𝐞𝐫 𝐚𝐧𝐠𝐥𝐞 𝐦𝐞𝐚𝐬𝐮𝐫𝐞𝐬.
l
m
Find the value of x.
15.)
1
( 𝑥 + 8) °
3
Decide whether the lines with the given equations are perpendicular, parallel, or neither.
16.)
𝑦 = −2𝑥 − 7
𝑦 = 2𝑥 + 7
19.)
17.)
𝑦 = 6𝑥 − 4
𝑦 = 6𝑥 + 8
18.)
2
𝑦 = 3𝑥 + 2
3
𝑦 = −2𝑥 + 2
Find the slope of the line passing through the points A(5, 3) and B(3, -1).
20.)
Write a two-column proof.
Given: ∠𝟏 ≅ ∠𝟑
Prove: ∠2 ≅ ∠4
21.)
Write a two-column proof.
̅̅̅̅ ≅ 𝐶𝐷
̅̅̅̅
Given: 𝐴𝐵
̅̅̅̅
̅̅̅̅
Prove: 𝐴𝐶 ≅ 𝐵𝐷
22.) Write a two-column proof.
⃗⃗⃗⃗⃗
Given: 𝑚∠1 = 𝑚∠3 = 37°, ⃗⃗⃗⃗⃗
𝐵𝐴 ⊥ 𝐵𝐶
Prove: 𝑚∠2 = 16°
23.) When you hang wallpaper, you use a tool called a plumb line to make sure one edge of the first strip of
wall paper is vertical. If the edges of each strip of wall paper are parallel and there are no gaps between the
strips, how do you know that the rest of the strips of wallpaper will be parallel to the first?