Online Test Banks
Score higher
See Online Test Banks
eLearning
Learning anything is easy
Browse Online Courses
Mobile Apps
Learning on the go
Explore Mobile Apps
Dummies Store
Shop for books and more
Start Shopping

Using the Hypotenuse-Leg-Right Angle Method to Prove Triangles Congruent

The HLR (Hypotenuse-Leg-Right angle) theorem — often called the HL theorem — states that if the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent. The following figure shows you an example.

image0.jpg

You can call this theorem HLR (instead of HL) because its three letters emphasize that before you can use it in a proof, you need to have three things in the statement column (congruent hypotenuses, congruent legs, and right angles).

Note: When you use HLR, listing the pair of right angles in a proof statement is sufficient for that part of the theorem; you don’t need to state that the two right angles are congruent.

Ready for an HLR proof? Well, ready or not, here you go.

image1.png

image2.jpg

Here’s a possible game plan. You see the pair of congruent triangles and then ask yourself how you can prove them congruent. You know you have a pair of congruent sides because the triangle is isosceles.

image3.png

Here’s the proof:

Statement 1:

image4.png

Reason for statement 1: Given.

Statement 2:

image5.png

Reason for statement 2: Definition of isosceles triangle.

Statement 3:

image6.png

Reason for statement 3: Reflexive Property.

Statement 4:

image7.png

Reason for statement 4: Given.

Statement 5:

image8.png

Reason for statement 5: Definition of altitude.

Statement 6:

image9.png

Reason for statement 6: Definition of perpendicular.

Statement 7:

image10.png

Reason for statement 7: HLR (using lines 2, 3, and 6)

Statement 8:

image11.png

Reason for statement 8: CPCTC.

Statement 9:

image12.png

Reason for statement 9: Definition of midpoint.

Statement 10:

image13.png

Reason for statement 10: Definition of median.

  • Add a Comment
  • Print
  • Share
blog comments powered by Disqus
Advertisement

Inside Dummies.com

Dummies.com Sweepstakes

Win $500. Easy.