Bellringer Find the slope going through the points.

Use the given information to write an equation for each line.

1.

2. (2, 3), (1, 6) 1. m=-2/3 2.m=3

3. slope 1/3 , y-intercept 2

4.

3. y=-1/3x-2 4.y=-3/2x+2

3-5 PARALLEL LINES AND TRIANGLES

Geometry: Chapter 3 Parallel and Perpendicular lines

Connections

Lesson Purpose

Objective Essential Question To use parallel lines to

prove a theorem about triangles.

To find measures of angles of triangles.

How do the postulates and theorem for proving triangles congruent shorten the time and work involved?

Postulate 3-3 Parallel Postulate Through any point not on a line,

there is one and only one line parallel to the given line.

There is exactly one line through Parallel to m.

P•

m

Triangle Angle-Sum Theorem 3-10

The sum of the measures of the angle of a triangle is 180.

Example #1 So we have

A+B+C=180 Using the angle measures we were given, we can substitute those values into our equation to get.

120+34+mC=180

mC=26

(1) Find the measure of ∠C.

. Using the diagram, we are given that mA= 120 mB=34

Example #2 (2) Find the

value of x in the diagram below.

mS=61 mT=73 mP=mQ=x

mS+mT+mSRT=180

61+73+mSRT=180 mSRT= 46 SRTQRP thus, QRP=46 P+Q+46=180 x+x+46=180 2x+46=180 P=Q=67

Key Concepts The angle formed by one

side of a triangle with the extension of another side is called an exterior angle of the triangle.

Key Concepts

Exterior angles get their name because they lie on the outsides of triangles.

The two angles that are not adjacent, or next to, the exterior angle of the triangle are called remote interior angles.

Triangle Exterior Angle Theorem 3-11 The Measure of

each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Example #31) Find the measures of ∠1 and ∠2 in the figure below.

Solution mS=42, and

mA=30 mS+mA+1=180 42+30+1=180 72+1=180 1=108 mS+mA= 2 42+30=2 2=72

Example #42) Find m∠B. Solution

R=93, and JEB=132

B=9x+3 R+B=JEB 93+(9x+3)= 132 96+9x=132 9x=36 x=4 B=39

Real World Connections

Summary-Recap The sum of the measures of the

angles of a triangle is equal to 180.

The measure of each exterior angle of a triangle equals the sum of the measures of its two remote interior angles.

Ticket Out and Homework

Ticket Out Homework pg.184-185 #s

10,14,20,24,25 What is true about the

measures of angles in a triangle?

By the Triangle Angle Sum theorem, The sum of the measures of the angles of a triangle are equal to 180