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Chapter 2 Terms
(some explanations and diagrams on the following pages)
2-1:
Vertical Angles
Adjacent Angles
Adjacent angles around a point
Linear Pair
Supplementary Angles
Complementary Angles
2-2 & 2-3:
Median & Midpoint
Angle Bisector
Altitude
Perpendicular Bisector
2-4:
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior Angles
The B-S Rule (a hint, not a reason)
2-5:
Auxiliary Lines
2-6:
Sum of the Angles in a Triangle
Exterior Angle
Isosceles Triangle
Equilateral Triangle
2-7:
Substitution Property
Subtraction Property
Formal Proofs - what should they look like?
Keywords & what they do
Vertical Angles: Create congruent angles
Statement: Vertical angles create congruent angles
<A = <D
Then write an equation to it the question
Supplementary angles: Add to 1800. Commonly found as a
linear pair.
Statement: Supplementary angles equal 1800
<A + <B = 1800
Then write an equation to it the question
Substitution Property: If two things (angles, segments,
numbers, etc) are equal to the same thing, they must be
equal to each other.
If <A = 1120 and <B = 1120, then <A = <B.
<A
112
°
112°
<B
Subtraction Property: Just like numbers or variable, the
measure of an angle or a segment can be subtracted.
A = 30°
If <A + <B = <C, then <A = <C - <B
B=
7
0°
C=1
00°
Keywords & what they do
Triangle Keywords
Medians: Create a midpoint; midpoints create two congruent
segments
Example: BD is a median
Statement: AD ~
= DC
Then write an equation to it
the question
Angle Bisectors: Create two congruent angles.
Example: AD is an angle bisector
Altitudes: Create right angles
Example: BD is an altitude
B
A
D
C
Statement: <BAD ~
= <CAD
Then write an equation to it
the question
Statement: <BDA is a right angle
or <BDC is a right angle
Then write an equation to it
the question
Perpendicular bisectors: Create right angles AND create
midpoints (which then create congruent segments)
Ex:
BD is a perpendicular bisector
Statement: <BDA is a right angle
or <BDC is a right angle
~ DC
or AD =
Then write an equation to it
the question
Keywords & what they do
Parallel Lines cut by a Transversal
Corresponding Angles: Match up in their position. They are
congruent.
Statement: Corresponding angles are congruent
<A ~
= <E
Then write an equation to it the example
Alternate Interior Angles: On opposite (alternate) sides of
the transversal, and inside (interior) of the parallel lines.
They are congruent.
Statement: Alternate Interior angles are congruent
<C ~
= <F
Then write an equation to it the example
Alternate Exterior Angles: On opposite (alternate) sides of
the transversal, and outside (exterior) of the parallel lines.
They are congruent.
Statement: Alternate Exterior angles are congruent
<A ~
= <H
Then write an equation to it the example
Same Side Interior Angles: On the same side of the
transversal, and inside (interior) of the parallel lines. They
are supplementary
Statement: Same Side Interior angles are supplementary
<D + <F = 1800
Then write an equation to it the example
Name: ______________________________________________________________
Date: _______________________
Period: _______
Directions: Answer the following questions completely on a separate
sheet of paper. DO NOT COMPLETE THE WORK ON YOUR IPAD!!! IT
MUST BE ON LOOSELEAF OR A NOTEBOOK!!! Make sure to show all
work. Justify your calculations for all questions!
1) In ΔABC, BD is an altitude drawn to side AC. If the m < BDA = 5𝑥 − 30, find the value of x.
2) In ΔWXY, XZ is the altitude drawn to side WY. Find the value of x if, m< Y = 2𝑥 − 5 and
m< ZXY = 2𝑥 + 21. Round to the nearest tenth, if necessary.
3) In triangle PQR, QS is a median. If PS = 4𝑥 − 2 and RS = 2𝑥 + 4. Find the value of x.
4) In ∆𝑄𝑅𝑆, segment QT is the bisector of < 𝑅𝑄𝑆. If 𝑚 < 𝑅𝑄𝑇 = 2𝑥 + 17 and 𝑚 < 𝑆𝑄𝑇 = 12𝑥 − 3, find the
value of x. Find 𝑚 < 𝑅𝑄𝑇.
5) In ∆ABC, BD is a perpendicular bisector. AD = 2y + 4 and CD = y + 12 and m<BDA = 5(x – 12).
Find the value of x and y. Justify your calculations.
6) In triangle ABC, AD is the median drawn to side BC. If BC=150 and DC=3𝑥 − 14, find the value of x.
Round your answer to the nearest tenth.
7) ⃗⃗⃗⃗⃗
𝐴𝐵 bisects <CAT. m<CAB = 2x – 2 and m<BAT = x + 6. Find m<CAT.
⃗⃗⃗⃗⃗⃗⃗ bisects right angle ABC. If the m<ABD is 6x – 3, then what is the value of x?
8) 𝐵𝐷
9) Point K is the midpoint of segment TJ. If the length of JK = 2x – 4 and the length of TK = x + 6. What is the
value of x? What is the length of segment TJ?
10) Two angles are supplementary. One angle is 30˚ more than another angle. Find both angles.
11) Lines AB and CD intersect at E. If m<AEC = 6x – 27 and m<BEC = 8x + 11,
find the measure of <BEC.
12) <J and <A are vertical angles. If the m<J = 3x+20 and the m<A = 5x-50, then what is the value of <J?
13) Lines AB and CD intersect at E. If m<AEC = x+30 and the m<DEB = 4x,
then what is the value of <AED?
Name: ______________________________________________________________
Date: _______________________
14) In the diagram below, m<ABC = 165˚. Find the value of x and m<CBD.
Period: _______
⃡⃗⃗⃗⃗⃗⃗⃗⃗ forms a straight angle. Using the diagram, find the m<DBC. Round to the
15) In the diagram below 𝐴𝐵𝐶
nearest tenth. (Not drawn to scale.)
16) Solve for x and y.
17) The measures of two supplementary angles are in the ratio 2:8. What is the measure of the larger angle?
18) <1 and <2 form a linear pair. The measure of <1 is 20 less than three times of <2. Find the measure of
the larger angle.
19) Use the diagram to answer the questions below:
a) Name an angle supplementary to < 𝐻𝑍𝐽 and
provide a reason for your calculation.
b) If 𝑚 < 𝐻𝑍𝐽 = 38°, what is the measure of each of the following
angles? Provide reasons for your calculations.
 < 𝐹𝑍𝐺
 < 𝐻𝑍𝐺
 < 𝐴𝑍𝐽
Name: ______________________________________________________________
Date: _______________________
20) Find the measures of each labeled angle. Give a reason for your solution.
21) In the diagram below m||n. Using the diagram, find the value of x.
22) In the diagram below m||n. Using the diagram, find the m<A.
23) Find the following angles for each question:
24) Find 𝑚 < 𝑏.
25) Find 𝑚 < 𝑛.
Period: _______
Name: ______________________________________________________________
26) Find the value of 𝑥.
Date: _______________________
Period: _______
27) In ΔABC, m<A = x, m<B = 2x + 2, and m<C = 3x + 4. What is the value of x?
28) In the diagram below, ΔABC is shown with AC extended through point D.
If m<BCD = 6x + 2, m<BAC = 3x + 15, and m<ABC = 2x – 1, what is the value of x?
(1) 12
(2) 14
10
11
(3) 16
(4) 18
1
9
29) The measures of the angles of a triangle are represented by 5x–7, 7x+6, and 4x–11. Find the value of x.
30) Find the value of x in the diagram below.
31) In the figure on the right, ̅̅̅̅
𝐴𝐵 ∥ ̅̅̅̅
𝐶𝐷 and ̅̅̅̅
𝐵𝐶 ∥ ̅̅̅̅
𝐷𝐸 . Prove that < 𝐴𝐵𝐶 = 𝑚 < 𝐶𝐷𝐸.
32) In the diagram below, prove that the sum of the labeled angles is 180°.