# Congruent Angles Theorems Worksheets

One of the first steps in understanding a geometric section if to determine if any figures in the section are congruent. If we can prove this, it tells us some measures that we may have been unsure of. We can then use this measure to deduce more measures within the system that are not part of those figures. It allows you to establish a standard of sorts. When we are working with triangles there are five methods for establishing congruence. In this section we will focus on using the theorems that we can use when we know the triangles possess a pair of congruent angles or that we can infer that they do. These worksheets and lessons teach you how to prove the congruency of triangles using the angle-side-angle and angle-angle-side theorems.

### Aligned Standard: High School Geometry - HSG-SRT.B.5

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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.

### What are the Congruent Angle Theorems: ASA and AAS?

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 measures of all three angles and sides of the triangle. To determine the congruence of triangles, we need to know at least three out of these six dimensions of the triangles.

We have five ways to verify the congruence of triangles: SSS (Side, Side, Side), SAS (Side, Angle, Side), ASA (Angle, Side, Angle), AAS (Angle, Angle, Side), and HL (Hypotenuse, Leg). The goal of this series is to explore the ASA and AAS theorems in depth.

ASA stands for 'angle, side, angle'. It implies that two triangles having two angles and an included side as equal. When we use this method, we know two of the three angles. we find out the third angles by taking the sum of the two known angles and subtract them from 180 degrees which is the sum of all the interior angles of a triangle. We then apply the law of sines to calculate the unknown sides. 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 the other triangle.

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 apply this method, we use the sum of the known angles and find the difference from 180 degrees to calculate the measure of the other angle. We then apply the law of sines to calculate each of the other unknown sides.

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.