In this example you have two angles marked with double lines telling you they are congruent. Two sides marked congruent with a single dash. Finally, you have a pair of vertical angle which are always congruent. As a result you have two congruent angle and an included side.

In this example you have two triangles that share a common side that is marked congruent. We have two angles at the top marked congruent, and two congruent right angles. Use "**ASA**" because you have two congruent angles and an included side.

In this example, notice you have two angles marked with double lines. This tells you that the angles are congruent. Next, you have two angles marked with a single line telling you these angles are congruent. Finally, you have a side between these angles with a single mark which tells you these two sides are congruent. So you have two angles and an included side, so use "**angle side angle**"

The video looks at four sets of triangles and shows you why you can use "ASA" to prove the triangles are congruent.

Side

Side

Side

Side

1.Use a *Given statement*

2. *Alternate interior angles* are congruent given *parallel sides.*

3.*Alternate interior angles* are congruent given *parallel sides.*

4. **Reflexive property of congruency**

5. *ASA Proof*

1.AB || CD

BC || DA

2.Angle BAC is congruent to Angle DAC

3. Angle BCA is congruent to angle DAC

4.Line segments AC is congruent to line segment CA

5. Triangle ABC is congruent to Triangle CDA

Angle

Angle

Angle

Angle

Side

Angle

Angle

Angle

Angle

Angle

Angle

Angle

Side

Angle

Side

Angle

When do you use "Angle Side Angle" ?

If you look carefully at "ASA" it is almost the opposite of "SAS"

Let's look at several examples, and why you can use "**ASA**".

Given AB || CD

BC || DA

Prove ΔABC ≌ ΔCDA

B

A

D

C

In order to show that trianles are congruent tic marks and arcs are used to show equal sides and angles.

Check out these examples of how triangles can be marked.

The sides are marked congruent with a single tic mark.

The angles are marked congruent with a single arc

The sides of this triangle are marked equal with a single tic mark.

The arrows tell you the sides are parallel

Angles and A and B are marked congruent with two arcs.

Angles D and C are marked congruent with a single arc

There are five ways used to determine if two triangles are congruent. **Angle side Angle (ASA)** is one of them.

The triangle has two angles and a side included between the two angles. When two or more triangles have an included side and any two angles that are equal then the triangles are congruent.