Congruent Triangles. Congruent figures- ◦ They have exactly the same shape. ◦ All parts of one...
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Transcript of Congruent Triangles. Congruent figures- ◦ They have exactly the same shape. ◦ All parts of one...
![Page 1: Congruent Triangles. Congruent figures- ◦ They have exactly the same shape. ◦ All parts of one figure are congruent to the corresponding parts of the.](https://reader036.fdocuments.us/reader036/viewer/2022072005/56649cee5503460f949bc617/html5/thumbnails/1.jpg)
Chapter 4Congruent Triangles
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Congruent figures- ◦ They have exactly the same shape.◦ All parts of one figure are congruent to the
corresponding parts of the other figure.◦ Corresponding sides and angles are congruent.
4.2 Apply Congruence and Triangles
A
B
C D F
E
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Name the congruent triangles.
Example
A
B
C
D
F
E
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Find x and y.
Example
ABCD FGHK
4x +2y 44
136
80
3x -6 in.9 in.
AD
CB G H
KF
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If 2 angles of one triangle are congruent to 2 angles of another triangle, then the third angles are also congruent.
Third Angle Theorem
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ExampleFind mYXW.
40
35X
ZW
Y
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ExampleProve: ACD CAB
Given: AD CB, DC BA, ACD CAB, CAD ACBA
C
B
D
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Side-Side-Side Congruence Postulate- If 3 sides of one triangle are congruent to 3 sides of a second triangle, then the two triangles are congruent.
4.3 Prove Triangles Congruent by SSS
K
L
M
N
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Side- Angle- Side Congruence Postulate – If 2 sides and the included angle of one triangle are congruent to 2 sides and the included angle of a second triangle, then the 2 triangles are congruent.
4.4 Prove Triangles Congruent by SAS and HL
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Given: KMMN,ML bisects KMNProve: KML NML
L N
M
K
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R is the center of the circle. Based on the diagram, what can you conclude about ∆URT and ∆SRT ?
Example
R
S T
U
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Why SSA does not work.
CD
B
A
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If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of a second triangle, then the 2 triangles are congruent.
Hypotenuse Leg Congruence Theorem
A
B C
D
F E
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Proof Prove: WYZ XZY
Given: WY XZ, WZ ZY, XY ZY
W
Z Y
X
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Angle- Side- Angle Congruence Postulate- If 2 angles and the included side of one triangle are congruent to 2 angles and the included side of a second triangle, then the 2 triangles are congruent.
4.5 Prove Triangles Congruent by ASA and AAS
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Angle- Angle- Side Congruence Theorem- If 2 angle and a non-included side of one triangle are congruent to 2 angles and the corresponding non-included side of a second triangle, then the two triangles are congruent.
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Right Angle Congruence Theorem- All right angles are congruent.
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Given: CBFCDF, BFFDProve: ABF EDF
F
C
A E
B D
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CPCTC- Corresponding Parts of Congruent Triangles are Congruent
4.6 Use Congruent Triangles