Mathematics
Grade 9
15 min
Congruent triangles: SSS, SAS, and ASA
Congruent triangles: SSS, SAS, and ASA
What you'll learn
- Identify whether two triangles are congruent by applying the SSS, SAS, or ASA congruence postulates, given a diagram or written description with sufficient information.
- Explain, in their own words, the meaning of each triangle congruence postulate (SSS, SAS, ASA) and how it is used to prove triangle congruence.
- Solve for unknown side lengths or angle measures in congruent triangles by setting up and solving algebraic equations, given that the triangles are congruent by SSS, SAS, or ASA.
- Determine if there is sufficient information provided in a diagram or description to prove triangles congruent using SSS, SAS, or ASA.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define triangle congruence and identify corresponding parts.
Explain the Side-Side-Side (SSS) Postulate and use it to prove triangles are congruent.
Explain the Side-Angle-Side (SAS) Postulate and use it to prove triangles are congruent.
Explain the Angle-Side-Angle (ASA) Postulate and use it to prove triangles are congruent.
Analyze given information to determine which congruence postulate (SSS, SAS, or ASA) applies to a pair of triangles.
Write a formal congruence statement, ensuring vertices are in the correct corresponding order.
Use congruence to determine unknown side lengths or angle measures in a triangle.
Have you ever wondered how manufacturers produce thousands of identical phone screens or how engineers build massive, stable bridges? 🌉 It a...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent TrianglesTwo triangles are congruent if all three of their corresponding sides are equal in length and all three of their corresponding angles are equal in measure. Essentially, they are identical in size and shape.If \triangle ABC has sides of 3, 4, 5 and angles of 90°, 53.1°, 36.9°, and \triangle XYZ has the same measurements, then \triangle ABC is congruent to \triangle XYZ.
Corresponding PartsThe matching sides and angles in two congruent triangles. If \triangle ABC \cong \triangle DEF, then \angle A corresponds to \angle D, side AB corresponds to side DE, and so on.In the statement \triangle CAT \cong \triangle DOG, the corresponding angle to \angle C is \angle D, and the corresponding side to segment AT is segment OG.
Side (S)A line segment that forms...
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Core Formulas
Side-Side-Side (SSS) Postulate
If three sides of one triangle are congruent to three sides of another triangle, then the two triangles are congruent.
Use this when you know the lengths of all three sides for both triangles. If side 1, side 2, and side 3 of the first triangle match side 1, side 2, and side 3 of the second, you can declare them congruent. For \triangle ABC and \triangle DEF, if AB \cong DE, BC \cong EF, and CA \cong FD, then \triangle ABC \cong \triangle DEF.
Side-Angle-Side (SAS) Postulate
If two sides and the *included* angle of one triangle are congruent to two sides and the *included* angle of another triangle, then the two triangles are congruent.
Use this when you have information about two sides and the angle *between them*. The position of the angle is...
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the tutorial, what is the fundamental definition of two congruent triangles?
A.They have the same area.
B.They are identical in size and shape, with all corresponding sides and angles being equal.
C.They have the same perimeter.
D.They have at least one pair of congruent sides and one pair of congruent angles.
Easy
Which postulate states that two triangles are congruent if three sides of one triangle are congruent to the three corresponding sides of another triangle?
A.Side-Side-Side (SSS) Postulate
B.Side-Angle-Side (SAS) Postulate
C.Angle-Side-Angle (ASA) Postulate
D.Angle-Angle-Angle (AAA) Postulate
Easy
If riangle ABC ≅ riangle XYZ, which side corresponds to side AC?
A.XY
B.YZ
C.XZ
D.ZX
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What grade level is "Congruent triangles: SSS, SAS, and ASA"?
Congruent triangles: SSS, SAS, and ASA is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Congruent triangles: SSS, SAS, and ASA?
You'll be able to: Identify whether two triangles are congruent by applying the SSS, SAS, or ASA congruence postulates, given a diagram or written description with sufficient information; Explain, in their own words, the meaning of each triangle….
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This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.