HL Triangle Congruence

HL Triangle Congruence

Multiple Choice

What is the hypotenuse?

• 8.2

• 2

• 5

Multiple Choice

What's the hypotenuse?

• 9

• 10.2

• 5

Multiple Select

Which are the legs?

• 9

• 11

• 14.2

Multiple Select

Which sides are the legs of the triangle?

• 19.2

• 12

• 15

Multiple Choice

The hypotenuse is the side

• at the bottom of the triangle

• across from the right angle

• I have no idea

Is triangle ABC congruent to DEF?

​

​Ask yourself three questions:

​1. Do you have a right triangle?

​2. Is the hypotenuse (The side across from the right angle) of the two triangles congruent?

​3. Is one leg (the sides that touch the right angle) of the two triangles cogruent?

Multiple Choice

Does HL work to prove the triangles are congruent?

• Yes

• No

Poll

How comfortable are you with HL?

• Not at all

• Somewhat

• Comfortable

Are these two triangles congruent?

Ask yourself:

​

1. Is at least one leg of each triangle congruent to each other?​

2. Are the two hypotenuses congruent to each other? ​

​

Don't forget about:

Reflexive Property of Congruence

​Whenever two triangles share a side, instantly think of Reflexive Property of Congruence!

​

​And separate the triangles!

​CA is congruent to CA by the Reflexive Property of Congruence

Are these two triangles congruent?

​Separate the triangles!

​

Then ask yourself:

​

1. Is at least one leg of each triangle congruent to each other?​

2. Are the two hypotenuses congruent to each other? ​

​

Multiple Choice

True or False

These two triangles are congruent by HL.

(Think about our two questions)

• False

• True

If we have two lines intersecting to form a right angle (90 degrees)....

​

Then the angle adjacent to it is also a right angle (90 degrees).

​

Multiple Choice

What other angle can you say is a right angle if $$\angle BNM$$   is a right angle ?

• $$\angle ABC$$  

• $$\angle ANM$$  

• $$\angle ANB$$  

• There are no other right angles.

​Angle ANB!

Why?

1. Do we have two lines intersecting to form 1 right angle?

2. Do we have another angle right next to the right angle?​

​

Is there any other right angles?

Ask yourself:

1. Do we have two lines intersecting to form 1 right angle?

2. Do we have another angle right next to the right angle?​

Multiple Choice

Is there any other right angles?

• $$\angle QSP$$  

• $$\angle RSP$$  

• $$\angle SQP$$  

• There are no other right angles

Are these two triangles congruent?

Ask yourself:

1. Does each triangle have one right angle?

2. Is at least one leg of each triangle congruent to each other?​

​

Multiple Choice

True or False: These two triangles are congruent by SSS

• True

• False

Multiple Choice

Can the HL Congruence Theorem be used to prove the triangles congruent? If so, write a congruence statement.

• Yes, △ABC≅△NLM
• Yes, △CBA≅△NLM
• Yes, △CBA≅△MLN
• No

Multiple Choice

What theorem would you use to show that the two triangles are congruent?

• SAS

• SSS

• HL

• AAS

Multiple Choice

When can we use the HL Congruence Theorem?

• Right Triangles

• Isosceles Triangles

• When we have a reflexive side

• SSA