perimeter = 31 npo = 50 ced = 55 de = 11 po = 33 uv = 36
TRANSCRIPT
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Perimeter = 31NPO = 50
CED = 55 DE = 11
PO = 33 UV = 36
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CED = 37 Perimeter = 40
DE = 18LM = 22
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REVIEW OF RIGHT TRIANGLES
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TRIA
NGLE C
ONGRUENCES
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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.
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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.
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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.
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PRACTICE
Which pairs of triangles below can be proven to be congruent by the AAS Congruence Theorem?
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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.)
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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.
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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.
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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.
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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.
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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.
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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.
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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.