Geometry Agenda Warm up

Mapquest 2

Interior/Exterior Triangle Angles Notes Practice

Session 5 Warm-upBegin at the word “Today”. Every Time you move, write down the word(s) upon which

you land.

Today

GO

JAGS!

is

homecoming!

school

Spirit!

your

Show

1. Move to the corresponding angle.2. Move to the vertical angle.3. Move to the supplementary angle.4. Move to the alternate interior angle.

.5. Move to the vertical angle6. Move to the alternate exterior angle.

7. Move to the consecutive exterior angle.

MAPQUEST 2

CCGPS Analytic Geometry

UNIT QUESTION: How do I prove geometric theorems involving lines, angles, triangles and parallelograms?Standards: MCC9-12.G.SRT.1-5, MCC9-12.A.CO.6-13

Today’s Question:If the legs of an isosceles triangle are congruent, what do we know about the angles opposite them?Standard: MCC9-12.G.CO.10

Triangles & AnglesTriangles & Angles

September 27, 2013September 27, 2013

Base Angles Theorem

If two sides of a triangle are congruent, then the angles opposite them are congruent.

If , thenACAB CB

Converse of Base Angles Theorem

If two angles of a triangle are congruent, then the sides opposite them are congruent.

If , thenCB ACAB

EXAMPLE 1 Apply the Base Angles Theorem

P

R

Q

(30)°

Find the measures of the angles.SOLUTION

Since a triangle has 180°, 180 – 30 = 150° for the other two angles.

Since the opposite sides are congruent, angles Q and P must be congruent.

150/2 = 75° each.

EXAMPLE 2 Apply the Base Angles Theorem

P

R

Q(48)°

Find the measures of the angles.

EXAMPLE 3 Apply the Base Angles Theorem

P

R

Q(62)°

Find the measures of the angles.

EXAMPLE 4 Apply the Base Angles Theorem

Find the value of x. Then find the measure of each angle.

P

RQ(20x-4)°

(12x+20)° SOLUTION

Since there are two congruent sides, the angles opposite them must be congruent also. Therefore, 12x + 20 = 20x – 4

20 = 8x – 4

24 = 8x

3 = x

Plugging back in,

And since there must be 180 degrees in the triangle,

564)3(20

5620)3(12

Rm

Pm

685656180Qm

LEG

LEG

HYPOTENUSE

Interior Angles Exterior Angles

Triangle Sum TheoremTriangle Sum TheoremThe measures of the three interior angles

in a triangle add up to be 180º.

x°

y° z°

x + y + z = 180°

54°

67°

R

S T

m R + m S + m T = 180º 54º + 67º + m T = 180º

121º + m T = 180º

m T = 59º

Find in RST.m T

85° x°55°

y°

A

B

C

D

E m D + m DCE + m E = 180º55º + 85º + y = 180º

140º + y = 180º

y = 40º

Find the value of each variable in DCE

Find the value of each variable.

x = 50º

x°

x° 43°

57°

Find the value of each variable.

x = 22º

(6x – 7)°43°55°

28°

(40 + y)°

y = 57º

Find the value of each variable.

x = 103º

62°

50°

50°

53°

x°

The measure of the exterior angle is equal to the sum of two nonadjacent interior angles

1

2 3

m1+m2 =m3

Exterior Angle TheoremExterior Angle Theorem

x

43

3881

148

72

x76

Ex. 1: Find x.

A. B.