Congruent Triangles

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Geometry

Congruent Triangles

2014-06-03



Table of Contents

Classifying Triangles Interior Angle Theorems Exterior Angle Theorems Isosceles Triangle Theorem Congruence & Triangles

SSS Congruence SAS Congruence ASA Congruence AAS Congruence HL Congruence Triangle Congruence Proofs CPCTC Triangle Coordinate Proofs

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Classifying Triangles

Return to Table of Contents

Parts of a triangle

C Vertex

Side opposite

interior

and are adjacent sides

Side

A Vertex

Side

B Vertex

Vertex (vertices) - points joining the sides of triangles

Adjacent Sides - two sides sharing a common vertex

Parts of a triangle (cont'd)

hypotenuse

leg

leg

leg base

leg

In a right triangle, the hypotenuse is the side opposite the right angle. The legs are the 2 sides that form the right angle.

In an isosceles triangle, the base is the side that is not congruent to the other two sides (legs).

If an isosceles triangle has 3 congruent sides, it is an equilateral triangle.

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Definitions

Polygon - a closed plane figure composed of line segments Triangle - three-sided polygon Sides - the line segments that make up a polygon Vertex (vertices) - the endpoints of the sides Acute Triangle - all angles < 90?

Obtuse triangle - one angle is between, 90? < angle < 180? Right Triangle - one 90? angle Equiangular Triangle - 3 congruent angles Equilateral Triangle - 3 congruent sides Isosceles Triangle - 2 congruent sides Scalene triangle - No congruent sides

A triangle is formed by line segments joining three noncollinear points. A triangle can be classified by its sides and angles.

Classification by Sides

Equilateral

Isosceles

Scalene

3 congruent sides 2 congruent sides

Classification by Angles Acute Equiangular

Right

No congruent sides Obtuse

3 acute angles

3 congruent angles (also acute)

1 right angle

1 obtuse angle

Classify the triangles by sides and angles

celicqkuilateral equiangular

scalene clicakcute

isosceles clicak cute

isosceles clicokbtuse

clickirsigohstceles

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Example

Measure and Classify the triangles by sides and angles

Slide 10 / 209

iCsColliisccckkefflooerrsA,Arnnigsswhwteerr

isoCCsclliieccklkefsfoo,rraAAcnunstsewweerr

sCCcllaiicclkeknffoeor,r AoAbnntssuwwseerr

Example

Measure and Classify the triangles by sides and angles

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scaCClelliincckek,ffoorbr AtAunnsssewweerr

scaCClellniiccekk, ffaoocrruAAtennsswweerr

equilateral, CClaliicckkutffeoo/rreAAqnunsisawwneegrrular

1 Classify the triangle with the given information: Side lengths: 3 cm, 4 cm, 5 cm

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

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Answer

2 Classify the triangle with the given information: Side lengths: 3 cm, 2 cm, 3 cm

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

3 Classify the triangle with the given information: Side lengths: 5 cm, 5 cm, 5 cm

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

4 Classify the triangle with the given information: Angle Measures: 30?, 60?, 90?

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

Answer

Answer

Answer

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