4.6 congruence in right triangles to prove triangles congruent using the hypotenuse leg theorem
TRANSCRIPT
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4.6 Congruence in Right Triangles• To Prove Triangles
Congruent using the Hypotenuse Leg Theorem
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Right Triangles…• In a Right Triangle the
side opposite the Right Angle is called the Hypotenuse.
• The Hypotenuse is always the largest side of the Right Triangle
• The other two sides are called the Legs.
• The Legs will always include the Right Angle.
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Side Side Angle?
•Remember SSA is not a Congruence Rule in All Triangles.
•It does work however in a special case, Right Triangles.
•It occurs when hypotenuses and one pair of legs are congruent.
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The HL Theorem!
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So…
To Use the HL Theorem, you must show that three conditions are met:1. There are two right triangles. (Right
Angles)2. The triangles have congruent
hypotenuses.3. There is one pair of congruent legs.
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Example 1
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Example 1B
•What two triangles are congruent by the Hypotenuse Leg (HL) Theorem? Write a Congruence Statement…
∆LMN ∆OQP
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Example 2: Using HL Theorem
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Ex 2B: Using HL• ΔXYZ is Isosceles. From Vertex X a
perpendicular Line is drawn intersecting YZ at point M.
• Explain why ΔXMY≅ΔXMZ…
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Example 3: Using HL Theorem
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Closure…
•How are SAS and HL Theorem alike? How are they Different?
•How does AAS Relate to HL Theorem? (Think Isosceles Triangles…)