Name: _____________________________________
Carnegie Geometry
Lesson 2-1, 2-2, 2-3 Quiz Review
Lesson 2-1: Introduction to Proof
1. Rewrite the following as a conditional statement, then circle the hypothesis and underline the conclusion. “The
sum of the measures of angle A and angle B is 90 degrees. Therefore, the angles are complementary.”
If the sum of the measures of angle A and angle B is 90 degrees, then the angles are complementary.
2. Sketch a figure to illustrate the given conditional statement. Then rewrite the conditional statement by
separating the hypothesis and conclusion into “Given” information and “Prove” information.
If <AXB is a right angle and ⃗⃗⃗⃗⃗
𝑋𝑌 bisects <AXB, then m<AXY = 45° and m<BXY = 45°.
Sketch:
⃗⃗⃗⃗⃗ bisects <AXB
Given: <AXB is a right angle and 𝑿𝒀
Prove: m<AXY = 45° and m<BXY = 45°
Lesson 2-2: Special Angles and Postulates
1. Draw a pair of supplementary angles that do not share a common side.
2. Draw a pair of complementary angles that share a common side.
3. Suppose that m<A = 66°, <B is complementary to <A, and <C is supplementary to <B. What are the measures of
angles B and C?
𝒎∠𝑩 = 𝟐𝟒° 𝒎∠𝑪 = 𝟏𝟓𝟔°
4. The variables x and y in the figure represent the measures of angles. Solve for x and y.
𝒙 = 𝟔𝟑°, 𝒚 = 𝟒𝟓°
5. The variables a and b in the figure represent the measures of angles. Solve for a and b.
𝒂 = 𝟑𝟎, 𝒃 = 𝟏𝟖
6. Name two pairs of adjacent angles in the figure.
∠WVX and ∠XVY, ∠XVY and ∠YVZ, ∠WVY and ∠YVZ, ∠WVX and ∠XVZ
7. What is the difference between two supplementary angles and two angles that form a linear pair?
Both supplementary angles and linear pairs have a total of 180°. Linear pairs MUST be adjacent, but
supplementary angles do not have to be.
8. Use the figure below to identify each of the following:
a) a pair of complementary angles
∠AGB and ∠BGC
b) two pairs of supplementary angles
There are lots!
c) four linear pairs
d) two pairs of vertical angles
Lots of these, too.
∠BGC and ∠FGE
9. Use the Segment Addition Postulate to create two statements about the figure below:
̅̅̅̅ + 𝒎𝑮𝑱
̅̅̅ = 𝒎𝑫𝑱
̅̅̅ + 𝒎𝑱𝑴
̅̅̅̅̅
̅̅̅̅, 𝒎𝑮𝑱
̅̅̅̅ = 𝒎𝑮𝑴
𝒎𝑫𝑮
10. Name the postulate that tells you that m<FGH + m<HGJ = m<FGJ in the figure below:
Angle Addition Postulate
Sec. 2-3: Forms of Proof
1. Identify the property that justifies each statement:
2. Enter the reasons to complete the two-column proof below:
3. The boxes below show the parts of a flow chart proof. Rearrange the boxes and draw arrows to connect the boxes in
a logical sequence to prove the statement.
Given: GH = HJ , FG = JK
Prove: FH = HK
4. Write the flow chart proof from above as a two column proof:
Statements
1. GH = HJ, FG = JK, HJ + JK = HK, FG = GH = FH
2. FG + GH = GH + JK
3. FG + GH = HJ + JK
4. FH = HK
Reasons
1. Given
2. Addition Property of Equality
3. Substitution
4. Substitution
5.
Vertical Angle Theorem