RHL

Thus far we have learned four shortcuts for determining if two triangles are congruent, namely _____, _____, _____ and _____. We have also learned that ASS does NOT work – it also not a very nice word. There is, however, one special case of SSA that does work. RHL (Right-Hypotenuse-Leg) Congruence Theorem

If the _____________________________________of one right triangle are congruent to the

_____________________________________ of a second right triangle, then the two triangles are

congruent.

SSSAASSAS ASA

Hypotenuse and one leg

Hypotenuse and one leg

The triangles at the right are congruent by RHL.

Hypotenuse Hypotenuse

Leg Leg

Example: Determine one more pair of angles or sides that would need to be congruent for the triangles to be congruent by the given congruence postulate/theorem.

1. ASA _______________

2. AAS _______________

3. RHL _______________

4. SAS _______________

F

E

D

A

B C

𝑎𝑛𝑔𝑙𝑒 𝐴≅ 𝑎𝑛𝑔𝑙𝑒𝐸𝑎𝑛𝑔𝑙𝑒𝐶≅ 𝑎𝑛𝑔𝑙𝑒 𝐷

𝐴𝐶≅ 𝐸𝐷𝐵𝐶≅ 𝐹𝐷

Example: Determine if each pair of triangles are congruent. If so, state why they are congruent and list the congruent triangles. If not, simply say “no”.

Given: ,DB AC DA DC Given: ,

int

DB AC

B is the midpo of AC

A B C

D

A B C

D

D

C

B

A

𝑅𝐻𝐿∆𝐵𝐴𝐷 ≅∆𝐵𝐶𝐷

∆ 𝐴𝐵𝐷 ≅∆𝐶𝐵𝐷∆𝐷𝐴𝐵≅ ∆𝐷𝐶𝐵

𝑆𝐴𝑆𝑅𝐻𝐿