Congruent Geometry Triangles

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New Jersey Center for Teaching and Learning

Progressive Mathematics Initiative?

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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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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

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Geometry

Congruent Triangles

2014-06-03



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Classifying Triangles

Return to Table of Contents

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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

Slide 9 / 209 Classify the triangles by sides and angles

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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

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Example

Measure and Classify the triangles by sides and angles

celicqkuilateral equiangular

scalene clicakcute

isosceles clicakcute

isosceles clicokbtuse

isosceles clickright

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Example

Measure and Classify the triangles by sides and angles

iCsColliisccckkefflooerrsA,Arnnigsswhwteerr

isoCCsclliieccklkefsfoo,rraAAcnunstsewweerr

sCCcllaiicclkeknffoeor,r AoAbnntssuwwseerr

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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

scaCClelliincckek,ffoorbr AtAunnsssewweerr

scaCClellniiccekk, ffaoocrruAAtennsswweerr

equilateral, CClaliicckkutffeoo/rreAAqnunsisawwneegrrular

Answer

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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

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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

Answer

Answer

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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

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5 Classify the triangle with the given information: Angle Measures: 25?, 120?, 35?

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

Answer

Answer

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6 Classify the triangle with the given information: Angle Measures: 60?, 60?, 60?

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

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7 Classify the triangle with the given information: Side lengths: 3 cm, 4 cm, 5 cm Angle measures: 37?, 53?, 90?

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

Answer

Answer

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8 Classify the triangle with the given information: Side lengths: 3 cm, 3 cm, 3 cm Angle measures: 60?, 60?, 60?

A Equilateral B Isosceles C Scalene

D Acute E Equiangular F Right G Obtuse

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10 Classify the triangle by sides and angles

A Equilateral

L

B Isosceles

C Scalene

D Acute

E Equiangular

F Right

G Obtuse

N

M

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12 An isosceles triangle is _______________ an equilateral triangle.

A Sometimes B Always C Never

Answer

Answer

Answer

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9 Classify the triangle by sides and angles

A Equilateral B Isosceles A C Scalene

B 120?

D Acute

E Equiangular

F Right C

G Obtuse

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11 Classify the triangle by sides and angles

A Equilateral

J

B Isosceles 85?

C Scalene

D Acute

E Equiangular

F Right G Obtuse

45? H

50? K

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13 An obtuse triangle is _______________ an isosceles triangle.

A Sometimes B Always C Never

Answer

Answer

Answer

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14 A triangle can have more than one obtuse angle. True False

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15 A triangle can have more than one right angle. True False

Answer

Answer

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16 Each angle in an equiangular triangle measures 60? True False

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17 An equilateral triangle is also an isosceles triangle True False

Answer

Answer

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Interior Angle Theorems

Return to Table of Contents

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T1. Triangle Sum Theorem

The measures of the interior angles of a triangle sum to 180? C

A

B

If you have a triangle, then you know the sum of its three interior angles is 180?

Why is this true? Click here to go to the lab titled, "Triangle Sum Theorem"

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