Congruent triangles

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17 Terms

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congruent figures

Figures that have the same size and shape

<p><span>Figures that have the same size and shape</span></p>
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Corollary to the Triangle Sum Theorem

The acute angles of a right triangle are complementary

<p>The acute angles of a right triangle are complementary</p>
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Corollary to a theorem

A statement that follows from already proven statement and requires little or no proof

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Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle is 180 degrees

<p>The sum of the measures of the interior angles of a triangle is 180 degrees</p>
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Exterior Angles Theorem

The measure of an exterior angle of the triangle is equal to the sum of the measures of the two no adjacent interior angles

<p>The measure of an exterior angle of the triangle is equal to the sum of the measures of the two no adjacent interior angles</p>
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CPCTC

Congruent Parts of Congruent Triangles are Congruent

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Third Angle Theorem

If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent

<p>If two angles of one triangle are congruent to two angles of a second triangle, then the third angles of the triangle are congruent </p>
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Base Angle Theorem (Isosceles Triangle)

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

<p>If two sides of a triangle are congruent, the angles opposite these sides are congruent.</p>
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Corollary to the Converse of the Base Angles Theorem

If a triangle is equiangular, then it is equilateral

<p>If a triangle is equiangular, then it is equilateral </p>
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Converse of the Base Angles Theorem

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

<p>If two angles of a triangle are congruent, then the sides opposite them are congruent.</p>
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Corollary to the Base Angles Theorem

If a triangle is equilateral, then it is equiangular

<p>If a triangle is equilateral, then it is equiangular </p>
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Congruent triangles

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

<p>2 triangles are congruent if and only if all pairs of corresponding sides and angles are congruent </p>
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SAS

If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent

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SSS

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

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AAS

if two angles and a non-included side of one triangle are congruent to the corresponding two angles and side of a second triangle, then the two triangles are congruent

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ASA

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

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HL Theorem (hypotenuse-leg)

If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and let of a second triangle, then the two triangles are congruent

<p>If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and let of a second triangle, then the two triangles are congruent</p>