Transcript Geometry - San Ramon Valley High School

Geometry
4.5 Other Methods of Proving
Triangles Congruent
B
A
We have 2 congruent angles and one congruent side………but the side is
not the included side. Can anything be proved?
In Chapter 3 you were introduced to this corollary:
if 2 angles of one triangle are congruent to 2 angles of
another triangle, then the 3rd angles are congruent.
This would allow us to conclude that angles A and B are congruent, and would
create an ASA congruence.
So the moral to the story is: any two congruent angles
and one congruent side gives you congruent triangles.
The AAS (Angle-Angle-Side)
Theorem
If two angles and a non-included side of one triangle
are congruent to the corresponding parts of another
triangle, then the triangles are congruent.
ABC

B
XYZ
C
A
X
Y
Z
Right Triangle Vocabulary
Remember the definition of a right triangle
LEG
It has one right angle
HYPOTENUSE
LEG
The HL (Hypotenuse - Leg)
Theorem
If the hypotenuse and a leg of one right triangle are
congruent to the corresponding parts of another right
triangle, then the triangles are congruent.
ABC

A
X
XYZ
B
C
Y
Z
Summary of Ways to Prove Triangles
Congruent
All triangles
SSS Post
SAS Post
ASA Post
AAS Thm
Right triangles
HL Thm
 <3
<1  <4
Given: <2
OVERLAPPING TRIANGLES
L
P
Q
1
Name the congruence
2
M
1
∆ LMN congruent
to ∆ PNM by ASA
same side
4
3
N
2
3
4
1. Given:
B  D
BC || AD
Prove:
DC  AB
B
A
C
D
3. Given: JAB  KBA
J
1   2
K
Prove: J  K
1
A
2
B
4. Given: Angles M and R are right angles
SR  TM
Prove:
S
T
M
R
SMR  TRM
Homework
pg. 142 CE #1-13
WE # 1-8
Bring Compass
Just a reminder of what’s allowed in the bins: EMPTY plastic bottles,
aluminum cans, and paper.
Whats NOT allowed: wrappers, gum, Ziploc baggies, half-empty beverages.
If these items are in the bins, then the whole bin gets dumped into the trash.
Last week, I spent the first 5 minutes of each class demonstrating what
goes in each receptacle. Since this small demonstration, my students have
been very good about proper placement of waste items in my classroom.
Let’s do a few from the homework
Turn to pg. 142 CE #5, #6 , #10
Now pg. 143 WE #2