Mathematics
Grade 10
15 min
SSS, SAS, ASA, and AAS Theorems
SSS, SAS, ASA, and AAS Theorems
What you'll learn
- Solve division problems with decimal quotients to the hundredths place using visual models (e.g., base-ten blocks, area models) with at least 80% accuracy.
- Explain the process of dividing a whole number by another whole number resulting in a decimal quotient, using place value understanding in their own words.
- Apply the standard algorithm for division to accurately calculate decimal quotients when dividing whole numbers to the tenths place in at least 4 out of 5 problems.
- Identify and correct errors in division problems involving decimal quotients, explaining the mistake in terms of place value or algorithm application.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the necessary conditions to prove triangle congruence using SSS, SAS, ASA, and AAS.
Apply the SSS, SAS, ASA, and AAS theorems to determine if two triangles are congruent.
Write a logical, step-by-step geometric proof to demonstrate triangle congruence.
Distinguish between valid congruence theorems and invalid shortcuts like SSA and AAA.
Correctly write a triangle congruence statement, ensuring corresponding vertices are in the correct order.
Identify what additional information is needed to prove two triangles are congruent.
Use the concept of 'Corresponding Parts of Congruent Triangles are Congruent' (CPCTC) after proving congruence.
How can a manufacturer produce thousands of identical triangular parts for a machine without measurin...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent TrianglesTwo triangles are congruent if all three corresponding sides and all three corresponding angles are equal. Congruent triangles are exact copies of each other in terms of size and shape.If ΔABC ≅ ΔDEF, it means AB = DE, BC = EF, AC = DF, ∠A = ∠D, ∠B = ∠E, and ∠C = ∠F.
Corresponding PartsThe sides and angles that are in the same relative position in two different figures. In a congruence statement like ΔABC ≅ ΔDEF, ∠A corresponds to ∠D, and side BC corresponds to side EF.In ΔPQR ≅ ΔXYZ, the side corresponding to PR is XZ.
Included AngleThe angle formed between two specified sides of a triangle.In ΔABC, ∠B is the included angle between sides AB and BC.
Included SideThe side located between two specified angles of a triangle.In ΔABC, side AC is the inc...
3
Core Formulas
SSS (Side-Side-Side) Congruence Theorem
If three sides of one triangle are congruent to the three corresponding sides of another triangle, then the two triangles are congruent.
Use this when you have information about all three pairs of corresponding sides and no information about angles.
SAS (Side-Angle-Side) Congruence Theorem
If two sides and the *included* angle of one triangle are congruent to the two corresponding sides and *included* angle of another triangle, then the two triangles are congruent.
Use this when you know two pairs of sides are congruent and the angle *between* those sides is also congruent.
ASA (Angle-Side-Angle) Congruence Theorem
If two angles and the *included* side of one triangle are congruent to the two corresponding angles and *included* s...
4 more steps in this tutorial
Sign up free to access the complete tutorial with worked examples and practice.
Sign Up Free to ContinueSample Practice Questions
Challenging
Given that ΔABC is an isosceles triangle with base AC, and BD is the angle bisector of ∠ABC. Which theorem is the most direct way to prove that ΔABD ≅ ΔCBD?
A.SSS
B.AAS
C.SAS
D.ASA
Challenging
In the figure, point C is the midpoint of AE and BD. Additionally, it is given that ∠A ≅ ∠E. Which theorem can be used to prove ΔABC ≅ ΔEDC?
A.ASA
B.SAS
C.AAS
D.SSS
Challenging
You are given that in ΔJKL and ΔMNO, JK ≅ MN and ∠K ≅ ∠N. Which single additional piece of information would allow you to prove the triangles are congruent, but by TWO different theorems (ASA and AAS)?
A.JL ≅ MO
B.∠J ≅ ∠M
C.KL ≅ NO
D.∠L ≅ ∠O
Want to practice and check your answers?
Sign up to access all questions with instant feedback, explanations, and progress tracking.
Start Practicing FreeMore from Congruent triangles
Mathematics for other grades
Frequently asked questions
What grade level is "SSS, SAS, ASA, and AAS Theorems"?
SSS, SAS, ASA, and AAS Theorems is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in SSS, SAS, ASA, and AAS Theorems?
You'll be able to: Solve division problems with decimal quotients to the hundredths place using visual models (e.g., base-ten blocks, area models) with at least 80% accuracy; Explain the process of dividing a whole number by another whole number….
Is "SSS, SAS, ASA, and AAS Theorems" free to practice?
Yes. You can read the tutorial preview for free, and signing up for a free ExcelOS account unlocks the full tutorial and all practice questions with instant feedback.
How many practice questions are included with SSS, SAS, ASA, and AAS Theorems?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.