Objectives: I will be able to…-Solve for missing angles and sides using properties of iso., equil., and right triangles

Vocabulary: Legs, base, base angles, vertex angle

You identified isosceles and equilateral triangles.

• Use properties of isosceles triangles.

• Use properties of equilateral triangles.

Vertex:

Adjacent Side:

Opposite Side:

Vertex: points joining the sides of the triangle.

Adjacent Side: sides sharing a common vertex.

Opposite Side: side opposite from the vertex.

Isosceles:Legs:

  Vertex Angle:  Base:  Base Angles: 

Isosceles: at least two congruent sidesLegs: congruent sides  

Vertex Angle: angle between legs  Base: non congruent side  Base Angles: angles adjacent to the base 

leg leg leg leg

vertex angle

leg leg

vertex angle

base

leg leg

vertex angle

base angles base angles

base

If 2 sides in a triangle are congruent, then the opposite base angles are congruent.

Base Angles Theorem:

A

B

C

C . A th e n,B CA B I f

If 2 base angles in a triangle are congruent, then the opposite sides are congruent.

Converse of Base Angles Theorem:

A

B

C

.B CA B th e nC , A I f

A

B

C

Q

R

S

80°

3x – 9

x + 5

2x + 7

1) In each triangle, solve for x and y.

x° y°

a) b)

50

x°y°

2) Solve for x and y.

x + x + 40 = 180 x =

70

y°

y + y + 110 = 180 y =

35

If a triangle is equilateral, then it is equiangular.

Corollary to Base Angles Theorem:

C . B A t h e n,C AB CA B I f

A

B

C

All angles are 60°

If a triangle is equiangular, then it is equilateral.

Corollary to Base Angles Theorem:

A

B

C

.C AB CA B t h e nC , B A I f

All angles are 60°

A

B

Cx° y°

z°

3) Solve for x, y, and z.

Right Triangle:

Hypotenuse: 

 Legs: 

 

Right Triangle: contains one right angle

Hypotenuse: side across from right angle longest side of the triangle

Legs: sides adjacent to the right angle leg

leg

hypotenuse

4) Classify the triangle by sides and angles.

A(5, 2) B (5, 6) C (1, 6)

A. PJM PMJ

B. JMK JKM

C. KJP JKP

D. PML PLK

A. Which statement correctly names two congruent angles?

A. Find mT.

Find x if ΔLMN is isosceles triangle with vertex angle L. If LM = 2x – 4, MN = 4x + 6, and LN = 3x – 14.

Which of the following is true if a||b?

5

4

A. m1 = m 5

B. m1 + m 2 = 180

C. m3 + m 4 = 180

D. m3 = m 5

ALGEBRA If m1 = 9x + 6, m2 = 2(5x – 3), and m3 = 5y + 14, find y.

A. y = 14

B. y = 20

C. y = 16

D. y = 24

A. Find mR.

B. Find PR.

containing the point (5, –2) in point-slope form?

Find the length of each side.

Solve for x.

SPORTS A pennant for the sports teams at Lincoln High School is in the shape of an isosceles triangle.

If the measure of the vertex angle is 18°, find the measure of each base angle.

BRIDGES Every day, cars drive through isosceles triangles when they go over the Leonard Zakim Bridge in Boston. The ten-lane roadway forms the bases of the triangles.

a. The angle labeled A in the picture has a measure of 67°. What is the measure of B?∠

b. What is the measure of C?∠ c. Name the two congruent sides.

A.

B.

C.

D.

containing the point (4, –6) in slope-intercept form?

A.

B.

C.

D.

A. The two horizontal lines are parallel.

B. The two vertical lines are parallel.

C. The vertical lines are perpendicular to the horizontal lines.

D. All of these statements are true.

GAMES In the game Tic-Tac-Toe, four lines intersect to form a square with four right angles in the middle of the grid. Is it possible to prove any of the lines parallel or perpendicular? Choose the best answer.

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