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## Congruent Triangles: SSS and SAS Theorems

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

What are Congruent Triangles: SSS and SAS Theorems? We all are familiar with a three-sided polygon with three straight sides and three angles known as a triangle. Below, we have elaborated on the congruence of triangles. CONGRUENCE OF TRIANGLES Two triangles are said to be congruent if they have the same angles and the same 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, three out of six (angles and sides) are sufficient information. 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 SSS and SAS theorems of congruent triangles SSS: SSS stands for 'side, side, side.' It implies that two triangles have all three sides exactly the same, ad we have to figure out the missing angles. To find out the angles of the SSS triangle: - we apply the Law of cosines to find out one of the angles. - then again, we apply the same law of cosine to calculate the second angle. - Finally, we use the known angles to add them to 180 degrees to calculate the last angle. In the above figure, if BC=PQ, AC=QR, AB=PR, then the triangle ABC is congruent to triangle PQR. Hence proving that the triangles are congruent if three sides of one triangle are equal to the three sides of another triangle. SAS: SAS stands for 'side, angle, side.' It means that two triangles have two sides and one angle between them are exactly the same. To find out the SAS congruence: - we apply the Law of cosines to find out one of the unknown sides. - then again, we apply the law of sine to calculate the smaller of the two angles. - Finally, we use the known angles to add them to 180 degrees to calculate the last angle. In the figure above, if BC=PR, AC=PQ, and angle P= angle C, then triangle ABC is congruent to triangle PQR. Hence proving that the triangles are congruent if the two sides and the included of one triangle is equal to the two corresponding sides and included angles. These worksheets and lessons focus on proving triangle congruence through the use of side-side-side and side-angle-side theorems.

### Printable Worksheets And Lessons  #### Homework Sheets

There is one homework for each theorem and the last one mixes both.

• Homework 1 - You can identify two triangles as being congruent when they are the same size and shape. SAS is another method for identifying congruent triangles.
• Homework 2 - Find the two triangles with two pairs of congruent sides and congruent included angles.
• Homework 3 - The three sides of ΔRTS are congruent to the three sides of ΔILU, so these triangles are congruent by the SSS Theorem.

#### Practice Worksheets

These are very quick ways to review proofs.

• Practice 1 - Which two triangles are congruent by the SAS Theorem? Complete the congruence statement.
• Practice 2 - Use the SSS Theorem here with this worksheet.
• Practice 3 - The SAS Theorem states that two triangles are congruent if and only if two sides and the included angle of one triangle are congruent to two sides and the included angle of the other triangle.

#### Math Skill Quizzes

It is all about finding the common sides on these problems.

• Quiz 1 - Using either SSS or SAS determine which triangles are congruent.
• Quiz 2 - To write the congruence statement, match the corresponding vertices. Since the side opposite R corresponding to the side opposite I, R corresponding to I.
• Quiz 3 - Use what you have learned to solve for what is presented.