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Geometry

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Geometry Triangle Congruence Theorems iRespond Question Master A.) Response A B.) Response B C.) Response C D.) Response D E.) Response E Percent Complete 100% 00:30 ... – PowerPoint PPT presentation

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Title: Geometry


1
Geometry
Triangle Congruence Theorems
2
Congruent Triangles
  • Congruent triangles have three congruent sides
    and and three congruent angles.
  • However, triangles can be proved congruent
    without showing 3 pairs of congruent sides and
    angles.

3
The Triangle Congruence Postulates Theorems
4
Theorem
  • If two angles in one triangle are congruent to
    two angles in another triangle, the third angles
    must also be congruent.
  • Think about it they have to add up to 180.

5
A closer look...
  • If two triangles have two pairs of angles
    congruent, then their third pair of angles is
    congruent.
  • But do the two triangles have to be congruent?

6
Example
Why arent these triangles congruent? What do
we call these triangles?
7
  • So, how do we prove that two triangles really are
    congruent?

8
ASA (Angle, Side, Angle)
  • If two angles and the included side of one
    triangle are congruent to two angles and the
    included side of another triangle, . . .

then the 2 triangles are CONGRUENT!
9
AAS (Angle, Angle, Side) Special case of ASA
  • If two angles and a non-included side of one
    triangle are congruent to two angles and the
    corresponding non-included side of another
    triangle, . . .

then the 2 triangles are CONGRUENT!
10
SAS (Side, Angle, Side)
  • If in two triangles, two sides and the included
    angle of one are congruent to two sides and the
    included angle of the other, . . .

then the 2 triangles are CONGRUENT!
11
SSS (Side, Side, Side)
  • In two triangles, if 3 sides of one are congruent
    to three sides of the other, . . .

then the 2 triangles are CONGRUENT!
12
HL (Hypotenuse, Leg)
  • If both hypotenuses and a pair of legs of two
    RIGHT triangles are congruent, . . .

then the 2 triangles are CONGRUENT!
13
HA (Hypotenuse, Angle)
  • If both hypotenuses and a pair of acute angles of
    two RIGHT triangles are congruent, . . .

then the 2 triangles are CONGRUENT!
14
LA (Leg, Angle)
  • If both hypotenuses and a pair of acute angles of
    two RIGHT triangles are congruent, . . .

then the 2 triangles are CONGRUENT!
15
LL (Leg, Leg)
  • If both pair of legs of two RIGHT triangles are
    congruent, . . .

then the 2 triangles are CONGRUENT!
16
Example 1
  • Given the markings on the diagram, is the pair of
    triangles congruent by one of the congruency
    theorems in this lesson?

D
E
F
17
Example 2
  • Given the markings on the diagram, is the pair of
    triangles congruent by one of the congruency
    theorems in this lesson?

18
Example 3
  • Given the markings on the diagram, is the pair of
    triangles congruent by one of the congruency
    theorems in this lesson?

19
Example 4
  • Why are the two triangles congruent?
  • What are the corresponding vertices?

SAS
?A ? ? D
?C ? ? E
?B ? ? F
20
Example 5
A
  • Why are the two triangles congruent?
  • What are the corresponding vertices?

SSS
B
D
?A ? ? C
?ADB ? ? CDB
C
?ABD ? ? CBD
21
Example 6
  • Given

Are the triangles congruent?
Why?
S S S
22
Example 7
  • Given

m?QSR m?PRS 90
  • Are the Triangles Congruent?

Why?
R H S
?QSR ? ?PRS 90
23
Summary
ASA - Pairs of congruent sides contained between
two congruent angles
AAS Pairs of congruent angles and the side not
contained between them.
SAS - Pairs of congruent angles contained between
two congruent sides
SSS - Three pairs of congruent sides
24
Summary --- for Right Triangles Only
HL Pair of sides including the Hypotenuse and
one Leg HA Pair of hypotenuses and one acute
angle LL Both pair of legs LA One pair of
legs and one pair of acute angles
25
THE END!!!
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