## Day 7 Right Triangles

### Objective:

1) Review the definition of a Right Triangle and the parts of
a Right Triangle

2) Right Triangle Congruence Theorems

### 1) Definition of Right Triangle

A triangle with one right angle

Parts of a Right Triangle

Hypotenuse-the side opposite the right angle

Legs-the other sides of the right triangle not opposite the right
angle

### 2) Construct two congruent right triangles and prove they
are congruent by SAS theorem. Since right triangles are special
cases, the SAS test for congruence can be adjusted to establish
a Leg-Leg Theorem.

### Leg-Leg (LL) Thm: If two legs of one right triangle are congruent
to the corresponding legs of another right triangle, then the
triangles are congruent

### Now prove the right triangles are congruent by the AAS theorem
using the hypotenuse as the side. Since right triangles are special
cases the AAS test for congruence can be adjusted to establish
a Hypotenuse-Acute Angle Theorem

### Hypotenuse-Acute Angle Thm: If the hypotenuse and an acute
angle of one right triangle are congruent to the hypotenuse and
corresponding angle of another right triangle, then the triangles
are congruent

### Next prove the right triangles are congruent by AAS theorem
and ASA theorem using one of the legs as the side. Since right
triangles are special cases the AAS test and the ASA test for
congruence can be adjusted to establish a Leg-Acute Angle Theorem

Leg-Acute Angle Thm: If one leg and an acute angle of a right
triangle are congruent to the corresponding leg and angle of another
right triangle, then the triangles are congruent

Hypotenuse-Leg Postulate: If the hypotenuse and a leg of one
right triangle are congruent to the hypotenuse and corresponding
leg of another right triangle, then the triangles are congruent