Congruency of shapes

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congruent triangles

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These are the things you should know for proving shapes(mostly triangles) are congruent.

16 Terms

1

congruent triangles

2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent

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2

congruent polygons

two polygons whose corresponding sides and angles are congruent when you name you must name corresponding verticals in order

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3

Third Angles Theorem

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent.

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4

Side-Side-Side (SSS)

If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

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5

Angle-Side-Angle (ASA)

If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent.

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6

AAS Theorem

If two angles and a non-included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

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7

isosoles triangle

has at least two congruent sides and two congruent angles

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8

Converse of the Isosceles Triangle Theorem

If two angles of a triangle are congruent, then the sides opposite those angles are congruent.

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9

Theorem 4-5 - Perpendicular Bisector Equidistant Theorem - PBET

If a line bisects the vertex angle of an isosceles triangle, then the line is also the perpendicular bisector of the base

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10

vertex

A point where two or more straight lines meet.

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11

collorary

Therom that proves a theorom

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12

Corollary to Theorem 4-3

If a triangle is equilateral, then the triangle is equiangular

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13

Corollary to theorem 4-4

If a triangle is equiangular, then the triangle is equilateral.

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14

Hypotenuse Leg Theorem

If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

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15

Conditions for HL theorem

  1. There are two right triangles

  2. The triangles have congruent hypotenuses

  3. There is one pair of congruent legs

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16

Hypotenuse

the side of a right triangle opposite the right angle

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