5.7 Other Ways to Prove Triangles Congruent

(Hypotenuse Leg Theorem)

I will begin with a review of the Angle-Angle-Side Congruence Theorem and why it works. I will go over their homework and any questions they may have on it. I will do a few review problems covering Angle Angle Side Congruence.

Okay class, what is the Congruence Theorem that doesn't work in most cases and that spells a word we don't use at school?

SSA, yes!

I have been telling you that this case doesn't work, right? I am going to show you why it doesn't work in most cases.

I will draw the picture on the board and lead them into the discovery that the SSA case works only in special cases, when you are dealing with right triangles.

So, a special case of SSA does work, right? This case deals only with right triangles and is called the Hypotenuse Leg Theorem.

What is right triangle?

A triangle that has a 90 degree angle in it.

What is a hypotenuse?

the side opposite the right angle

What are the legs?

the sides opposite the acute angles in a right triangle

(I will make sure to right these definitions on the overhead for them to copy down.)

We will do some examples to make sure they understand the distinction between hypotenuse and legs of a right triangle and make sure they realize these only apply to right triangles.

Okay, so the Hypotenuse Leg Theorem says that if you have a hypotenuse and one leg of a right triangle congruent to the hypotenuse and leg of another right triangle, then the triangles are congruent.

We will practice doing some examples involving the Hypotenuse Leg congruence case. I will emphasize to the students that every time you see two right triangles that look congruent, you can't just assume that they are congruent by Hypotenuse Leg, but that you could have Side-Angle-Side Congruence for two right triangles, etc. I will again reemphasize how the ORDER MATTERS when stating two triangles congruent but that it doesn't matter when labeling segments or angles. If time permits, we will throw in some other Angle-Angle-Side Congruence examples. Near the end of class, I will pass out a Section 5.7 worksheet for them since we have completed this section now. I will explain to them how it covers proving triangles congruent using the Angle-Angle-Side Congruence Theorem and the Hypotenuse Leg Congruence Theorem.

I will summarize by revisiting what a hypotenuse and leg is of a right triangle. I will restate what the HL Theorem is and how it is a special case involving right triangles when the SSA case does work.