Download Geometry - Unit 1 - Lesson 1.4

Geometry
Unit 1: Lesson 1.4
Name: _______________________________
Date: _________________ Period: _______
Special Angles
Essential Questions:
o
How do algebra and geometry work together within the coordinate plane?
Goal:
 I can understand an algebraic relationship exists between: adjacent segments, adjacent angles, and
special angle pairs.
Key Ideas/Vocabulary:
Diagram:

Vertical Angles 

Complementary Angles 

Supplementary Angles 

Linear Pairs 
o
Postulates/Theorems:
 Postulate 11 – Linear Pair Postulate
 If two angles form a linear pair, then they are supplementary, i.e., the sum of
their measures is 1800.
 Theorem 2.1 – Congruent Supplements Theorem
 If two angles are supplementary to the same angle or to congruent angles,
then they are congruent.
 Theorem 2.2 – Congruent Complements Theorem
 If two angles are complementary to the same angle or to congruent angles,
then they are congruent.
 Theorem 2.3 – Vertical Angles Theorem
 If two angles are vertical angles, then they are congruent.
Section 1: Identifying Special Pairs of Angles
1) Use the terms defined above to describe
YT 1) Use the terms defined above to describe
relationships between the labeled angles.
relationships between the labeled angles.
Answer:
2
1
5 4
3
Answer:
Section 2: Angle Measures
2) Find the measures of two supplementary angles if
the measure of one angle is 6 less than five times the
other angle.
YT 2) Find the measures of two complementary
angles if one angle measures eleven degrees more
than seven times the measure of the other.
Answer:
Answer:
3) Find mSQT and mTQR .
YT 3) Find mAEC and mCEB .
Answer: mSQT =
mTQR =
4) A supplement of an angle is six times as large as a
complement of the angle. Find the measures of the
angle, its supplement, and its complement.
Answer: mAEC =
Answer:
5) Find the measure of angles 1, 2, 3, 4, and 5. Angle 4
and 500 are complementary.
Answer:
YT 5) BD bisects ABC. Find mABD and find
mABC.
A
mCEB =
YT 4) Find x and y.
B
5
Answer:
x2 – 3x
44+4x
xx+ 6 D
C
m1  _______, m2  _______, m3  _______,
m4  _______, m5  _______
Answer:
Section 3: Interpret Figures
6) Determine whether each statement can be assumed
from the figure below. TRUE or FALSE.
YT 6) Determine whether each statement can be
assumed from the figure below. TRUE or FALSE.
Answers:
_____a.) mVYT  90 
_____b.) TYW and TYU are supplementary.
_____c.) VYW and TYS are adjacent angles.
_____d.) TYW and VYS are linear pairs.
Homework:
mABD =
Answers:
_____a.) mXAY  90 
_____b.) TAU and UAY are complementary.
_____c.) UAX and UXA are adjacent angles.
_____d.) ZAT and TAU are linear pairs.
Special Angles – Supplement Worksheet # 6
Lesson Summary:
mABC =
Name______________________________________________Period__________Date____________________
SPECIAL ANGLES - SUPPLEMENT WORKSHEET # 6
Complementary and Supplementary Angles
1. If A and B are complementary and mA = 36, find mB
2. A and B are complementary, mA = 3x + 11 and mB = 2x + 19. Find…
a. x =
b. mA =
c. mB =
3. If A and B are supplementary and mA = 56, find mB
4. If an angle is acute, what can you say about its supplement?
5. If mA = 4x + 31 and mB = 2x – 7, what is the measure of each angle if they are
supplementary?
For #’s 6 – 9 use the diagram above.
6. If m1 = 100, find m2 = ___ and m4 =
.
7. If m2 = 56, find m1 =
.
and m3 =
8. If m3 = 145, find m2 = ___ and m4 =
.
9. If m4 = 37, find m1 =
.
___ and m3 =
For #’s 10 – 14, use the diagram provided.
2
1
10. Name the complement of 1. _______________
3
11. Name 2 angles complementary to 2. ______________
12. If m2 = 36, find m1 =
and m3 =
13. If m2 = 17, find m1 =
and m3 =
14. What can you conclude about 1 and 3? ______________________________
Vertical Angles
15. m1 = 2x + 6, m3 = 3x -4
x=
1
4
2
m1 =
3
m2 =
m3 =
m4 = _____
16. m2 = 5x – 10, m4 = 3x + 16
17. m1 = 3x +12, m2 = 2x + 3
x=
x=
m1 =
m1 =
m2 =
m2 =
m3 =
m3 =
m4 =
m4 =