Download 4.1 Triangle Congruence

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)
4x-6 = 2x + 18
Given
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
Triangles- Come in 3 types:
Obtuse:
Acute:
An acute triangle
has 3 acute
angles
An obtuse triangle has 1
obtuse angle
Right:
A right triangle has 1
right angle.
Sub groups
-Scalene Triangle
no congruent sides.
Equilateral
all sides are congruent.
Isosceles
Triangle
Triangle
at least 2 congruent sides.
You can have Scalene and Isosceles of each type of triangle!
Triangles
List each type of triangle
Acute
Scalene
Obtuse
Scalene
Isosceles
Equilateral
Right
Isosceles
Scalene
Isosceles
Triangles
Sketch 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). 180°
Cut 2 of the vertices (angles) from the triangle.
Line up all three vertices. What do you notice?
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
180°
in every triangle is _______.
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
x  52  55  180

x

x  107  180

52°
55°
x  73



Example #2
x  60  50  180
z
x
130°
50°
x  110  180
x  70
100°
60°
120°
z  70  180
z  110
Example #3
B
Find mA, mB, mC.
x+7
x  x  7  2 x  9  180
4 x  2  180
4 x  182
x  45.5
x
A
2x-9
C
mA  45.5
mB  52.5
mC  82
Example #4
Find w.
w
x
48°
x
48  x  x  180
48  2 x  180
2 x  132
x  66
w  66  90
w  24
Example #5
Find mA, mB, mC.
3x  13  4 x  25  2 x  7  180
9 x  45  180
9 x  135
x  15
B
4x+25
3x+13
A
mA  58
mB  85
2x+7
C
mC  37
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