4.1 Warm up

1. Using deductive reasoning prove the following:

4x -6 = 2(x + 9)

2) 6, 17, 28, 39….. Find the function rule and the 50th term

3) With parallel lines, certain relationship exist for the type of angles formed. List the type of angles that are created and their relationship.

Answers

1) 4x-6 = 2(x+9) Given

4x-6 = 2x + 18 Distributive Prop

2x – 6 = 18 Subtraction prop. of equality

2x = 24 Addition prop. of equality

x = 12 Division prop. of equality

2) 6, 17, 28, 39…… nth term = f(n) = 11n – 5 50th term = 545

3) Vertical angles, corresponding angles, alt. exterior, alt interior are congruent

Same side interior, same side exterior, linear pairs add to 180

Sub groups -Scalene Triangle no congruent sides.

Equilateral Triangle all sides are congruent.

Isosceles Triangle at least 2 congruent sides.

Triangles- Come in 3 types: Acute: Obtuse: Right:

An acute triangle has 3 acute angles

An obtuse triangle has 1 obtuse angle

A right triangle has 1 right angle.

You can have Scalene and Isosceles of each type of triangle!

Triangles

Acute Obtuse Right

Scalene Isosceles

Equilateral

Scalene Isosceles Scalene Isosceles

List each type of triangle

TrianglesSketch each type of triangle in the box

Ex. 1 - Triangles

How do I sketch, label, and mark each figure?A) Right Isosceles triangle SUN

with SU = UN.

B) Obtuse Isosceles triangle SEA

with SE = EA.

Triangles class work!

Page 64-65 Questions #2-20

More to come……stay tuned!

4.1 Triangle Congruence

Year 2 Geometry

Materials

You will need: Protractor Scissors

Investigation #1

Draw a triangle using your straight edge of the protractor. Make a variety of sizes!

Measure each angle of the triangle to the nearest 10°. The sum of the interior angles equals to ?

Cut out the triangle (around the perimeter). Cut 2 of the vertices (angles) from the triangle. Line up all three vertices. What do you notice?

180°

They form a line. (180°)

Investigation #1 – continued

Paste the three vertices lined up in your notes and complete the following conjecture.

Triangle Sum Conjecture

The sum of the measures of the interior angles in every triangle is _______.180°

Third Angle Conjecture

If two angles of one triangle are equal in measure to two angles in another triangle, then the third angle in each triangle is ___________________________?equal in measure

Example #1

52°55°

x

73

180107

1805552

x

x

x

Example #2

120°

130°

100°

z

60°

50°

x

110

18070

70

180110

1805060

z

z

x

x

x

Example #3

5.45

1824

18024

180927

x

x

x

xxx

C.B, mA, mm Find

x 2x-9

x+7

A

B

C

82

5.52

5.45

Cm

Bm

Am

Example #4

w. Find

66

1322

180248

18048

x

x

x

xx

48°

w

xx

24

9066

w

w

Example #5

C.B, mA, mm Find

15

1359

180459

18072254133

x

x

x

xxx

3x+13 2x+7

4x+25

A C

B

37

85

58

Cm

Bm

Am

Example 6

With a partner create your own problem with triangles similar to the previous examples to share with your group.

Summary

Write the Triangle Sum Conjecture in your own words.

In – Class Work

Lesson 4.1 – workbook Homework: Triangle Sum HW pg 201-202

2-5,8,9, 14-16