4 4 isosceles triangles corollaries cpctc
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4.4 Isosceles Triangles, Corollaries, & CPCTC PowerPoint PPT Presentation


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4.4 Isosceles Triangles, Corollaries, & CPCTC. Isosceles Triangles. Has at least 2 congruent sides. The angles opposite the congruent sides are congruent Converse is also true. The sides opposite the congruent angles are also congruent. This is a COROLLARY.

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4.4 Isosceles Triangles, Corollaries, & CPCTC

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4 4 isosceles triangles corollaries cpctc

4.4 Isosceles Triangles,Corollaries, &CPCTC


Isosceles triangles

Isosceles Triangles

  • Has at least 2 congruent sides.

  • The angles opposite the congruent sides are congruent

  • Converse is also true.The sides opposite the congruent angles are also congruent.

  • This is a COROLLARY.

    A corollary naturally follows a theorem or postulate. We can prove it if we need to, but it really makes a lot of sense.


4 4 isosceles triangles corollaries cpctc

Vertex angle

Base

  • The bisector of the vertex angle of an isoscelesΔ is the perpendicular bisector of the base.

In addition, you just learned that the angles opposite congruent sides are congruent…


Corresponding parts

B

F

That means that EG  CB

A

E

What is AC congruent to?

FE

G

C

Corresponding parts

When you use a shortcut (SSS, AAS, SAS, ASA, HL) to show that 2 triangles are ,

that means that ALL the corresponding parts are congruent.

EX: If a triangle is congruent by ASA (for instance), then all the other corresponding parts are .


Corresponding parts of congruent triangles are congruent

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.

Corresponding parts of congruent triangles are congruent.


4 4 isosceles triangles corollaries cpctc

Corresponding Parts of Congruent Triangles are Congruent.

If you can prove congruence using a shortcut, then you KNOW that the remaining corresponding parts are congruent.

CPCTC

You can only use CPCTC in a proof AFTER you have proved congruence.


For example

Statements Reasons

AC  DF Given

C  F Given

CB  FE Given

ΔABC  ΔDEF SAS

AB  DE CPCTC

For example:

A

Prove: AB  DE

B

C

D

F

E


Using cpctc

Using CPCTC

  • History According to legend,

  • one of Napoleon’s officers used

  • congruent triangles to estimate

  • the width of a river. On the

  • riverbank, the officer stood up

  • straight and lowered the visor

  • of his cap until the farthest thing

  • he could see was the edge of the

  • opposite bank. He then turned

  • and noted the spot on his side

  • of the river that was in line with

  • his eye and the tip of his visor


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