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Transcript
NPO = 50
Perimeter = 31
CED = 55
PO = 33
DE = 11
UV = 36
CED = 37
DE = 18
Perimeter = 40
LM = 22
REVIEW OF RIGHT TRIANGLES
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.
PRACTICE
Determine whether each pair of triangles can be proven congruent. If so, write a
congruence statement and name the postulate or theorem used.
1.
2.
3.
4.
5.
6.
WARM UP
Determine whether each pair of triangles can be proven congruent. If so, write a
congruence statement and name the postulate or theorem used.
7.
8.
9.
10.