Download Theorems

Bellwork

What is the distance between the points (5,4) & (-3,2)

What is the midpoint of the segment that extends from
(4,-1) to (3,2)

What is the linear equation of the line perpendicular to y=4x-2
and goes through the point (24,12)
Bellwork Solution

What is the distance between the points (5,4) & (-3,2)
2 17

What is the midpoint of the segment that extends from
(4,-1) to (3,2)
7 1
 , 
2 2

What is the linear equation of the line perpendicular to y=4x-2
and goes through the point (24,12)
1
y   x  18
4
Finding Triangle Congruence
Methods via Constructions
Section 4.3, 4.4, 4.5
Findings?
Today we saw that of these methods, only four actually work consistently.
They are:
Side-Side-Side
Angle-Angle-Angle
Side-Angle-Side
Angle-Side-Angle
Hypotenuse-Leg
Side-Angle-Angle
Side-Side-Angle
Theorems
Postulate 19: Side-Side-Side Congruence Postulate
If three sides of one triangle are congruent to three sides of a second
triangle, then the two triangles are congruent…
Postulate 20: Side-Angle-Side Congruence Postulate
If two sides and the included angle of one triangle are congruent to two
sides and the included angle of a second triangle, then the two triangles are
congruent
Theorem 4.5: Hypotenuse-Leg Congruence Theorem
If the hypotenuse and a leg of a right triangle are congruent to the
hypotenuse and a leg of a second right triangle, then the two triangles are
congruent
Note: This theorem only works for right triangles
Theorems
Postulate 21: Angle-Side-Angle Congruence Postulate
If two angles and the included side of one triangle are congruent to two
angles and the included side of a second triangle, then the two triangles are
congruent
Theorem 4.6: Angle-Angle-Side Congruence Theorem
If two angles and non-included side of one triangle are congruent to two
angles and the corresponding non-included side of a second triangle, then
the two triangles are congruent
Examples
These triangles are congruent via what method?
Examples
These triangles are congruent via what method?
Homework

4.4


2, 9-18, 31-33
4.5

2-7, 14-21, 23-24
Most Important Points

Theorems and Postulates that govern triangle
congruence