Angle Relationship in Triangles and Quadrilaterals

[Pages:15]MPM 1D ? Unit 7: Geometric Relationships ? Lesson 1

Date: ______________

Learning goal: how to apply angle relationships to find missing angles in triangles and quadrilaterals.

Angle Relationship in Triangles and Quadrilaterals

REVIEW: GRADE 8 THEOREMS

Opposite Angle Theorem (OAT) - opposite angles are ____________

Complementary Angles (CA) - two angles add up to ______________

Supplementary Angles (SA) - two angles add up to _________

Angle Sum Triangle Theorem (ASTT) - three angles in a triangle add up to _________

Isosceles Triangle Theorem (ITT) - angles opposite the equal sides are _________

Equilateral Triangle Theorem (ETT) - all three sides equal and all three angles are________

Exterior Angle Theorem (EAT) - exterior angle of a triangle is equal to the sum of the interior and non-adjacent angles

Angle Sum Quadrilateral Theorem (ASQT) - four angles in a quadrilateral add up to

_________

Example 1: State the measure of the supplementary angle for each of the following angles.

a) 40?

b) 170?

c) 93?

Example 2: State the measure of the complementary angle for each of the following angles.

a) 14?

b) 64?

c) 1?

Example 3: Determine the measure of each indicated angle. State your reasoning.

a)

b)

c)

z

67?

44?

c a

57? b

36 95

b

Example 4: Determine the value of x, and then the measure of each angle. State your reasoning.

a)

b)

2x

x

3x

25x-7 23x+7

EXTERIOR ANGLES

Exterior Angles of Triangles and Quadrilaterals

The exterior angles of a triangle add to

.

The exterior angles of a quadrilateral add to

.

Proof:

Example 5: Determine the size of each indicated angle. State your reasoning.

30

95

a)

b)

d

y

c

x

95

105

4y

Assignment 7.1: Angle Relationships in Triangles and Quadrilaterals

1. Determine the measure of each indicated angle, state your reasoning.

a)

b)

c)

82? 33?

t z r

37?

a 127? b

100? 85?

y x

z 51?

117?

d)

97? a

e)

f)

y e

d

\\

//

y

80?

55?

x

b

c 76?

82?

80? x 42?

2. Find the value of x, then find the measure of the unknown angle.

a)

b)

A

A B

D

B

C C

3. Determine the value of the variables, state your reasoning.

a)

b)

105? 40?

z y 28? x

28

x

?

72 y

?

7.1 Answers:

1. a) z = 65? , r = 65? , t = 78?

b) a = 122? , b = 53?

d) a = 83? , b = 98? , c = 104? , d = 75? , e = 105?

c) x = 66? , y = 114? , z = 129? e) x = 55? , y = 70? f) x=580, y=420

2. a) x = 20, ................
................

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