Right Triangles 4-3B

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Right Triangles 4-3B

• What are the additional congruence theorems used
  only for right triangles?
• Which combination of sides for triangles in
  general cannot be used but works for right
  triangles?

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If you need to prove that two right triangles are
congruent, you can use any of the triangle
congruence postulates. However, there are some
additional postulates just for right triangles
which are special cases for what you already know.
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Leg-Leg Congruence Theorem (LL)
If the legs of a right triangle are congruent to
the legs of another right triangle, then the two
triangles are congruent. (Same as SAS)
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Hypotenuse Acute Angle Congruence Theorem (HA)
If the hypotenuse and an acute angle of one right
triangle are congruent to the hypotenuse and an
acute angle of another right triangle, then the
two triangles are congruent. (SAA)
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Leg Acute Angle Congruence Theorem (LA)
If one leg and one acute angle of a right
triangle are congruent to the corresponding legs
and acute angle of another right triangle, then
the two triangles are congruent. (ASA)
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Hypotenuse Leg Congruence Theorem (HL)
If the hypotenuse and a leg of one right triangle
are congruent to the hypotenuse and a leg of
another right triangle, then the two triangles
are congruent.
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Proof
Statements

• Reasons
• Given
• Per lines form rt angles
• Def rt ?
• Given
• Reflexive
• HL

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• What are the additional congruence theorems used
  only for right triangles?
• Leg-Leg (LL)
• Hypotenuse-Angle (HA)
• Leg-Angle (LA)
• Hypotenuse-Leg (HL)
• Which combination of sides for triangles in
  general cannot be used but works for right
  triangles?
• Hypotenuse-Leg (HL)

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Assignment 4-3B

• Page 295, 1-9, 15, 19