Perimeter = 31NPO = 50

CED = 55 DE = 11

PO = 33 UV = 36

CED = 37 Perimeter = 40

DE = 18LM = 22

REVIEW OF RIGHT TRIANGLES

TRIA

NGLE C

ONGRUENCES

ASA (ANGLE-SIDE-ANGLE) POSTULATE

If two angles and the included side in one triangle are congruent to two angles and

the included side in another triangle, then the two triangles are congruent.

PRACTICE

In each pair below, the triangles are congruent. Tell which triangle congruence postulate allows you to conclude that they are congruent, based on the markings in the figures.

AAS (ANGLE-ANGLE-SIDE) POSTULATE

If two angles and a nonincluded side of one triangle are congruent to the

corresponding angles and nonincluded side of another triangle, then the

triangles are congruent.

PRACTICE

Which pairs of triangles below can be proven to be congruent by the AAS Congruence Theorem?

THREE OTHER POSSIBILITIES

• AAA combination—three angles• Does it work?

• SSA combination—two sides and an angle that is not between them (that is, an angle opposite one of the two sides.)

SPECIAL CASE OF SSA

When you try to draw a triangle for an SSA combination, the side opposite the given angle can sometimes pivot like a swinging door between two possible positions. This “swinging door” effect shows that two triangles are possible for certain SSA information.

A SPECIAL CASE OF SSA

If the given angle is a right angle, SSA can be used to prove congruence. In this case, it is called the Hypotenuse-Leg Congruence Theorem.

HL (HYPOTENUSE-LEG) CONGRUENCE THEOREM

If the hypotenuse and a leg of a right triangle are congruent to the Hypotenuse and a leg of another right triangle, then

the two triangles are congruent.

OTHER RIGHT TRIANGLE THEOREMS

LL (LEG-LEG) Congruence Theorem If the two legs of a right triangle are congruent to the corresponding two legs of another right triangle, then the triangles are congruent.

LA (LEG-ANGLE) Congruence Theorem If a leg and an acute angle of a right triangle are congruent to the corresponding leg and acute angle of another right triangle, then the triangles are congruent.

OTHER RIGHT TRIANGLE THEOREMS

HA (HYPOTENUSE-ANGLE) Congruence Theorem If the hypotenuse and an acute angle of a right triangle are congruent to the corresponding hypotenuse and acute angle of another triangle, then the triangles are congruent.

HL (HYPOTENUSE-LEG) Congruence Theorem If the hypotenuse and a leg of a right triangle are congruent to the corresponding hypotenuse and leg of another right triangle, then the triangles are congruent.

PRACTICEDetermine whether each pair of triangles can be proven

congruent. If so, write a congruence statement and name the postulate or theorem used.

1.

3.

5.

2.

4.

6.

WARM UPDetermine whether each pair of triangles can be proven

congruent. If so, write a congruence statement and name the postulate or theorem used.

8.

10.

7.

9.