Date post: | 04-Aug-2015 |
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Education |
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If the hypotenuse and a leg of one right triangle are congruent to the corresponding hypotenuse and a leg of another triangle, then the triangles are congruent.
HyL (Hypotenuse-Leg) Congruence
Theorem
B C
D
A
Given: BCAD ACBA
ACDABD Prove:
PROOFStatement Reasons
Perpendiculars form right angles
A triangle with a 90 angle is a right triangle
Given
AD = AD Reflexive
Hypotenuse-leg Postulate
ACBA
ADCADB
nglesright tria are ADCandADB
nglesright tria are ADCandADB
HyA(Hypotenuse-Acute angle) Congruence
TheoremIf the hypotenuse and an acute angle of one right triangle are congruent to the corresponding hypotenuse and an acute angle of another right triangle, then the triangles are congruent
CB
A
R
P
Q
Given:
Prove:
PQAB B Q
C and R are right angles
PQRABC
PROOFStatement Reasons
Given
Any two right angles are congruent
HyA Congruence Theorem
PQRABC
PQAB B Q
C and R are right angles
C R