Mathematics
Grade 10
15 min
Proving triangles congruent by ASA and AAS
Proving triangles congruent by ASA and AAS
What you'll learn
- Identify the key information needed to solve a division word problem with a decimal quotient with 80% accuracy.
- Solve division word problems involving decimals to the hundredths place with at least 70% accuracy, showing all work.
- Explain the meaning of the decimal quotient in the context of a word problem, using complete sentences, in at least 2 out of 3 opportunities.
- Apply the correct units to the decimal quotient when solving division word problems, consistently doing so in all practice problems.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the included side between two angles in a triangle.
Differentiate between the Angle-Side-Angle (ASA) Postulate and the Angle-Angle-Side (AAS) Theorem.
Determine if ASA or AAS can be used to prove two triangles are congruent based on given information.
Write a formal two-column proof to show triangle congruence using the ASA Postulate.
Construct a logical argument in a two-column proof to demonstrate triangle congruence using the AAS Theorem.
Apply ASA and AAS congruence to solve for unknown side lengths or angle measures in geometric figures.
How can engineers guarantee that a triangular bridge support is stable and identical to others without measuring every single part? 🌉 It's all about geometric shortcuts!
This tutorial will teach you t...
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Key Concepts & Vocabulary
TermDefinitionExample
Congruent TrianglesTwo triangles are congruent if all three corresponding sides and all three corresponding angles are equal in measure. Essentially, they are exact copies of each other.If \triangle ABC \cong \triangle DEF, then \angle A \cong \angle D, \angle B \cong \angle E, \angle C \cong \angle F, \overline{AB} \cong \overline{DE}, \overline{BC} \cong \overline{EF}, and \overline{AC} \cong \overline{DF}.
Included SideThe side of a triangle that is located between two specified angles.In \triangle XYZ, the side \overline{XY} is the included side between \angle X and \angle Y.
Non-included SideA side of a triangle that is not located between two specified angles.In \triangle XYZ, the side \overline{YZ} is a non-included side for the pair of angles \angle X and \an...
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Core Formulas
Angle-Side-Angle (ASA) Congruence Postulate
Given \triangle ABC and \triangle DEF. If \angle A \cong \angle D, \overline{AC} \cong \overline{DF}, and \angle C \cong \angle F, then \triangle ABC \cong \triangle DEF.
Use this when you can prove that two pairs of corresponding angles and the side *between* them are congruent. The 'S' is physically located between the two 'A's in the triangle.
Angle-Angle-Side (AAS) Congruence Theorem
Given \triangle ABC and \triangle DEF. If \angle A \cong \angle D, \angle B \cong \angle E, and \overline{BC} \cong \overline{EF}, then \triangle ABC \cong \triangle DEF.
Use this when you can prove that two pairs of corresponding angles and a side that is *not* between them are congruent. The 'S' is adjacent to only o...
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Challenging
You are given △ABC with ∠A = 50° and ∠B = 70°. Which of the following pieces of information is NOT sufficient to prove △ABC ≅ △DEF, given △DEF has ∠D = 50° and ∠E = 70°?
A.¯¯¯¯AB ≅ ¯¯¯¯DE
B.¯¯¯¯BC ≅ ¯¯¯¯EF
C.¯¯¯¯AC ≅ ¯¯¯¯DF
D.∠C ≅ ∠F
Challenging
In a figure, △ABE and △DCE are proven congruent by AAS. It is given that ∠A ≅ ∠D and ∠AEB ≅ ∠DCE. As a result of the congruence, we can state that ¯¯¯¯AE ≅ ¯¯¯¯DC by CPCTC. This fact is then used to prove that △ADE ≅ △DAF. What concept is being demonstrated?
A.The transitive property of congruence.
B.Using CPCTC as a bridge to prove further congruences.
C.The reflexive property of congruence.
D.The definition of an isosceles triangle.
Challenging
Given: ∠1 ≅ ∠2 and ¯¯¯¯HK bisects ∠FHG. To prove △FKH ≅ △GKH by ASA, what must be the missing reason for the statement ¯¯¯¯HK ≅ ¯¯¯¯HK?
A.Given
B.Definition of Midpoint
C.Symmetric Property of Congruence
D.Reflexive Property of Congruence
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What grade level is "Proving triangles congruent by ASA and AAS"?
Proving triangles congruent by ASA and AAS is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Proving triangles congruent by ASA and AAS?
You'll be able to: Identify the key information needed to solve a division word problem with a decimal quotient with 80% accuracy; Solve division word problems involving decimals to the hundredths place with at least 70% accuracy, showing all….
Is "Proving triangles congruent by ASA and AAS" free to practice?
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How many practice questions are included with Proving triangles congruent by ASA and AAS?
This lesson includes 24 practice questions across multiple difficulty levels, each with instant feedback and explanations.