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## Congruent Triangles: ASA and AAS Theorems

#### Trigonometry - HSG-SRT.B.5

What are Congruent Triangles: ASA and AAS Theorems? Two triangles are said to be congruent if they have identical three angles and three sides. But in most cases, we aren't given all the three angles and sides of the triangle. To find the congruence of triangles, we need to know at least three out of six dimensions of triangles. We have five ways to estimate the congruence of triangles: SSS (Side, Side, Side), SAS (Side, Angle, Side), ASA (Angle, Side, Angle), AAS (Angle, Angle, Side), and HL (Hypotenuse, Leg) below, we have discussed ASA and AAS theorems of congruent triangles. ASA:ASA stands for 'angle, side, angle'. It implies that two triangles having two angles and an included side as equal. To find out the ASA congruence of triangles: - we find out the third angles by adding three angles to 180 degrees - then apply the law of sines to calculate the unknown sides is congruent to: The triangles are congruent if two angles and the included side of one triangle are equal to the corresponding two angles and included side of another triangle AAS: AAS stands for 'angle, angle, side'. It means that we know that two angles and the non-included side of two triangles are exactly the same. To find out the AAS triangle: - we use the three angle and add to180 degrees to calculate the other angle - then apply the law of sines to calculate each of the other unknown sides In the above figure, if AC=QP, angle Q= angle A and angle B= angle R, then triangle ABC is congruent to triangle QPR Hence proving that the triangles are congruent if two angles and the non-included side of one triangle are equal to the corresponding two angles and non-included of another triangle. These worksheets and lessons teach you how to prove the congruency of triangles using the angle-side-angle and angle-angle-side theorems.

### Printable Worksheets And Lessons

• ASA Step-by-step Lesson - Find the two triangles that have angle-side-angle going for them.

• Guided Lesson - As usual, I focus on the theorem that I left out in the lesson.

• Guided Lesson Explanation - I have been getting a few responses from teachers asking me if I can color more of the sheets like this one. I guess red really does it for you?

• Practice Worksheet - Find the congruency and the theorem that proves it.

• Matching Worksheet - This makes you remember the labels found on the triangles.  #### Homework Sheets

Homework 1 and 2 focus on an individual theorem. Homework 3 looks at both of them.

• Homework 1 - The ASA Theorem states that two triangles are congruent if and only if two angles and the included side of one triangle are congruent to two angles and the included side of the other triangle.
• Homework 2 - Find the two triangles with two pairs of congruent angles and congruent included sides.
• Homework 3 - Start by identifying all the sides and then all the angles.

#### Practice Worksheets

Find the triangles that match the criteria given.

• Practice 1 - Which two triangles are congruent by the ASA Theorem? Complete the congruence statement.
• Practice 2 - To write the congruence statement, match the corresponding vertices.
• Practice 3 - Two angles and the included side of a triangle are congruent to two angles and the included side of another triangle, so these triangles are congruent by the ASA theorem.

#### Math Skill Quizzes

See which congruence statement fits best.

• Quiz 1 - Which two triangles are congruent by the AAS Theorem?
• Quiz 2 - ASA is the shorthand way of describing the angle-side-angle theorem.
• Quiz 3 - AAS is the shorthand way of describing the angle-angle-side theorem.