Angles in Triangles

Angles in Triangles

A review of Unit 7

Types of Triangles

Triangles are classified by angle sizes and the number of congruent sides.

Angle Sizes:

Equiangular, Acute, Right, Obtuse

Congruent Sides:

Equilateral, Isosceles, Scalene

Multiple Choice

What kind of triangle is this?

• Obtuse Isosceles

• Right Isosceles

• Acute Scalene

• Acute Isosceles

• Obtuse Scalene

Multiple Choice

What type of triangle is shown?

Select all that apply

• Acute Scalene

• Right Isosceles

• Right Scalene

• Obtuse Isosceles

• Acute Isosceles

Multiple Choice

What type of triangle is shown?

• Acute Scalene

• Obtuse Isosceles

• Equilateral

• Right Isosceles

• Right Scalene

Multiple Choice

What type of triangle is shown?

• Obtuse Isosceles

• Right Isosceles

• Equilateral

• Acute Isosceles

• Equilateral

Multiple Choice

What type of triangle is shown?

• Obtuse Isosceles

• Right Isosceles

• Equilateral

• Obtuse Scalene

• Acute Scalene

Multiple Choice

What type of triangle is shown?

• Right Isosceles

• Right Scalene

• Equilateral

• Obtuse Scalene

• Acute Isosceles

Multiple Choice

What type of triangle is shown?

• Acute Isosceles

• Right-Scalene

• Equilateral

• Acute Scalene

• Obtuse Scalene

Triangle Sum Theorem

The sum of the interior angles of a triangle is 180 degrees

Multiple Choice

What is the measure of the missing angle?

• 82
• 43
• 55
• 180

Multiple Choice

Find the measure of the missing angle.

• 47

• 57

• 53

• 133

Multiple Choice

Solve for x.

• 5

• 12

• -7

• -6

Multiple Choice

Solve for x.

• 16

• 11

• 50

• 6

Multiple Choice

Solve for x THEN find the degrees for angle A.

• 44^o

• 96^o

• -14^o

• 63^o

Multiple Choice

Solve for x

• 28
• 12
• 10
• 2

Multiple Choice

Find the value of x

• 16

• 2

• 6

• 8

Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two remote interior angles.

Multiple Choice

What is the measure of x?

• 101°

• 111°

• 121°

• 131°

Multiple Choice

Find the indicated angle measure. (What is ?)

• 51°

• 37°

• 167°

• 41°

Multiple Choice

Set up an equation to find x.

• 42 + 8x = 2 + 12x

• 2 + 12x + 42 = 8x

• 42 + 8x + 2 + 12x = 180

• 42 + 8x = 180

Multiple Choice

Solve for x

• 2

• 2.2

• 10

• 11

Multiple Choice

Set up an equation to find x.

• 52 + 5x + 16 + 10x + 8 = 180

• 52 - 5x + 16

• 52 + 5x + 16 = 10x + 8

• 52 + 10x + 8 = 5x +16

Four Parts of an Isosceles Triangle

• Legs - the two congruent sides

• Base - the side that is not a leg

• Vertex Angle - angle where legs meet

• Base Angles -two angles on the base

Multiple Select

Which segments are the legs?

• Segment AB

• Segment BC

• Segment AC

Multiple Choice

Which segment is the base?

• Segment AB

• Segment BC

• Segment AC

Multiple Choice

Which angle is the vertex angle?

• Angle A

• Angle B

• Angle C

Multiple Select

Which angles are the base angles?

• Angle A

• Angle B

• Angle C

Triangle Inequality Theorem

The sum of the two smallest sides of a triangle must be larger than the third side.

Three Possible Outcomes

• T-Rex Arms - Two smaller sides add up to less than the third side

• Line Segment - Two smaller sides add up to equal the third side

• Triangle - Two smaller sides add up to more than the third side

Multiple Select

Which of the following sets of side lengths could produce a triangle. SELECT ALL THAT APPLY.

• 4, 4, 4

• 5, 5, 10

• 3, 6, 9

• 5, 7, 11

• 13, 5, 6

Multiple Choice

Will these three sides form a triangle? 7, 8, 12

• yes

• no

Multiple Choice

Will these line segments form a triangle? 7, 8, 15

• yes

• no

If you are only given two sides and you are asked to find the RANGE of values for the third side...

• Subtract the two values

• Add the two values

• The third side will be between those to answers

• EX: 15,20,?

• 20 - 15 = 5 ........... 20 + 15 = 35

• Third side is bigger than 5 and smaller than 35

Multiple Choice

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 mm, 4 mm

• more than 3 but less than 11

• more than 11 but less than 3

• less than 3 but more than 11

Multiple Choice

Given are the lengths of two sides of a triangle. Find the range of lengths for the third side. 7 ft, 13 ft

• more than 6 but less than 20

• more than 20 but less than 6

• less than 6 but more than 20

Isosceles Triangle Theorems

The base angles of an Isosceles triangle are congruent

The Line of Symmetry is also...

Median

Altitude

Angle Bisector

Perpendicular Bisector

Multiple Choice

Find the value of y

• 100

• 180

• 40

• 50

Multiple Choice

Find the value of y.

• 180

• 19

• 9

• 4.5

Multiple Choice

Find the value of y?

• 16

• 12

• 4

• 8

Multiple Choice

Find the value of x

• 55

• 135

• 125

• 25

Multiple Choice

Find the value of x

• 112

• 68

• 80

• 86

Multiple Choice

Find the value of x

• 90

• 180

• 45

• 15

Multiple Choice

Find the value of x

• 11

• 7

• 4

• 15

Multiple Choice

Find the value of x

• 6

• 12

• 2

• 72

Multiple Choice

Find the value of x

• 18

• 180

• 25

• 30

Multiple Choice

Find the value of x

• 10

• 52

• 9

• 7