Geometry Unit 6 Review

Front 1

Triangle Sum Theorem (4.1)

Back 1

The sum of the measures of the interior angles of a triangle is 180 degrees. m<A+m<B+m<C=180

Front 2

Exterior Angle Theorem (4.2)

Back 2

The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles. m<1=m<A+m<B

Front 3

Corollary to the Triangle Sum Theorem

Back 3

The acute angles of a right triangle are complementary. m<A+m<B=90

Front 4

Third Angles Theorem (4.3)

Back 4

If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. if <A=<D & <B=<E, then <C=<F

Front 5

Properties of Congruent Triangles (Reflexive, Symmetric, Transitive)(Theorem 4.4)

Back 5

REFLEXIVE: Every triangle is congruent to itself.
SYMMETRIC: if <ABC=<DEF, then <DEF=<ABC
TRANSITIVE: if <ABC=<DEF & <DEF=<JKL, then <ABC=<JKL

Front 6

Side-Side-Side (SSS) Congruence Postulate (19)

Back 6

If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Front 7

Side-Angle-Side (SAS) Congruence Postulate (20)

Back 7

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

Front 8

Angle-Side-Angle (ASA) Congruence Postulate (21)

Back 8

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.

Front 9

Angle-Angle-Side (AAS) Congruence Theorem (4.5)

Back 9

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

Front 10

Base Angle Theorem (4.6)

Back 10

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

Front 11

Converse of the Base Angles Theorem (4.7)

Back 11

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

Front 12

Corollary to the Base Angles Theorem (4.6)

Back 12

If a triangle is equilateral, the it is equiangular.

Front 13

Corollary to the Converse of the Base Angles Theorem (4.7)

Back 13

If a triangle is equinangular, then it is equilateral.

Front 14

Hypotenuse-Leg (HL) Congruence Theorem (4.8)

Back 14

If the hypotenuse and a lef of a right triangle are conguent to the hypotenuse and a lef of a second right triangle, then the two triangles are congruent.

Front 15

Midsegment Theorem (5.9)

Back 15

The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long.

Front 16

Longer Side Theorem (5.10)

Back 16

If one side of a triangle is longer than another side, then the angle opposite the longer side is larger than the angle opposite the shorter side.

Front 17

Largest Angle Theorem (5.11)

Back 17

If one angl of a traingle is larger than another angle, then the side opposite the larger angle is longer than the side opposite the smaller angle.

Front 18

Exterior Angle Inequality (5.12)

Back 18

The measure of an exterior angle of a triangle is greater than the measure of either of the two nonadjacent interior angles.

Front 19

Triangle Inequality Theorem (5.13)

Back 19

The sum of the lengths of any two sides of a triangle isreater than the length of the third side.

Front 20

Hinge Theorem (5.14)

Back 20

If two sides of one triangle are congruent to two sides of another triangle, and the included angle of the frst is larger than the included angle of the second, then the third side of the first is longer than the third side of the second.

Front 21

Converse of the Hinge Theorem (5.15)

Back 21

If two sides of one triangle are congruent to two sides of another tirangle, and the third side of the first is longer than the third side of the second, then the included angle of the first is larger than the included angle of the second.

Front 22

Polygon Ratio Theorem (8.1)

Back 22

If two polygons are similar, then the ratio of their perimeters is equal to the ratios of their corresponding side lengths.