4.6 Congruence in Right Triangles• To Prove Triangles

Congruent using the Hypotenuse Leg Theorem

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.

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.

The HL Theorem!

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.

Example 1

Example 1B

•What two triangles are congruent by the Hypotenuse Leg (HL) Theorem? Write a Congruence Statement…

∆LMN ∆OQP

Example 2: Using HL Theorem

Ex 2B: Using HL• ΔXYZ is Isosceles. From Vertex X a

perpendicular Line is drawn intersecting YZ at point M.

• Explain why ΔXMY≅ΔXMZ…

Example 3: Using HL Theorem

Closure…

•How are SAS and HL Theorem alike? How are they Different?

•How does AAS Relate to HL Theorem? (Think Isosceles Triangles…)