This document discusses four theorems for proving right triangle congruence: the LL Theorem, LA Theorem, HyL Theorem, and HyA Theorem. It provides the conditions for proving two right triangles are congruent using side-side-side, side-angle-side, hypotenuse-leg, or hypotenuse-angle congruence. It then gives an example problem to show triangle congruence using a statement of correspondence.

1. Lesson 3.4:
Right Triangle
Congruence

2. Hypotenuse
– longest side and
always the side
opposite the right
angle
leg
leg
right
angle
acute
angle
acute
angle
RIGHT TRIANGLE

3. LL Congruence Theorem

4. If 𝐀𝐂 ≅ 𝐃𝐅,
𝐂𝐁 ≅ 𝐅𝐄,
then ∆ABC≅∆DEF
by LL Theorem

5. LA Congruence Theorem

6. If 𝐀𝐂 ≅ 𝐃𝐅,
∠A≅∠D,
then ∆ABC≅∆DEF
by LA Theorem

7. HyL Congruence Theorem

8. If 𝐀𝐂 ≅ 𝐃𝐅,
𝐀𝐁 ≅ 𝐃𝐄,
then ∆ABC≅∆DEF
by HyL Theorem

9. HyA Congruence Theorem

10. If ∠B≅∠E,
𝐀𝐁 ≅ 𝐃𝐄,
then ∆ABC≅∆DEF
by HyA Theorem

11. SEATWORK #1:
Show that the two triangles are congruent by writing a
conditional statement of correspondence.
2.
1.
B
A T
M
E N

12. 4.
3.
5.
K
I
M
J
U N
P
E T
A
C