Mathematics
Grade 10
15 min
Similarity rules for triangles
Similarity rules for triangles
What you'll learn
- Identify the pattern when dividing numbers by 10, 100, and 1,000 by recognizing how the decimal point shifts to the left.
- Solve division problems involving whole numbers and decimals divided by 10, 100, and 1,000 with at least 80% accuracy.
- Explain how the value of a digit changes when a number is divided by 10, 100, or 1,000, using mathematical vocabulary like 'place value' and 'decimal point'.
- Apply the pattern of dividing by powers of ten to solve real-world problems involving measurement and money, showing their work.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify the conditions required for the Angle-Angle (AA), Side-Angle-Side (SAS), and Side-Side-Side (SSS) similarity rules.
Apply the AA, SAS, and SSS similarity rules to determine if two triangles are similar.
Write a correct similarity statement (e.g., ΔABC ~ ΔXYZ) that reflects the correspondence between vertices.
Set up and solve proportions to find unknown side lengths in similar triangles.
Use the properties of similar triangles to find unknown angle measures.
Construct a formal proof to demonstrate that two triangles are similar.
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This tutorial will introduce the three fundamental shortcuts for provi...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar TrianglesTriangles that have the same shape but not necessarily the same size. This means their corresponding angles are congruent (equal) and their corresponding sides are in proportion.If ΔABC ~ ΔXYZ, then ∠A ≅ ∠X, ∠B ≅ ∠Y, ∠C ≅ ∠Z, and AB/XY = BC/YZ = AC/XZ.
Corresponding PartsThe angles and sides of two triangles that are in the same relative position. In a similarity statement like ΔABC ~ ΔXYZ, ∠A corresponds to ∠X, and side AB corresponds to side XY.In ΔPQR ~ ΔLMN, the side corresponding to PR is LN.
Similarity Ratio (or Scale Factor)The constant ratio between the lengths of corresponding sides of two similar triangles.If ΔABC has sides 3, 4, 5 and similar ΔXYZ has sides 6, 8, 10, the similarity ratio of ΔABC to ΔXYZ is 3/6 = 1/2.
ProportionAn equation...
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Core Formulas
Angle-Angle (AA) Similarity Postulate
If ∠A ≅ ∠X and ∠B ≅ ∠Y, then ΔABC ~ ΔXYZ.
If two angles of one triangle are congruent to two angles of another triangle, the triangles are similar. This is the most frequently used similarity rule.
Side-Angle-Side (SAS) Similarity Theorem
If ∠A ≅ ∠X and (AB/XY) = (AC/XZ), then ΔABC ~ ΔXYZ.
If an angle of one triangle is congruent to an angle of another triangle and the lengths of the sides that include these angles are proportional, the triangles are similar.
Side-Side-Side (SSS) Similarity Theorem
If (AB/XY) = (BC/YZ) = (AC/XZ), then ΔABC ~ ΔXYZ.
If the corresponding side lengths of two triangles are all proportional, the triangles are similar.
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Easy
Which condition is sufficient to prove that two triangles are similar by the Angle-Angle (AA) Similarity Postulate?
A.Two pairs of corresponding sides are proportional.
B.Two pairs of corresponding angles are congruent.
C.One pair of corresponding angles is congruent.
D.All corresponding sides are congruent.
Easy
According to the Side-Side-Side (SSS) Similarity Theorem, two triangles are similar if all three pairs of their corresponding sides are what?
A.Congruent
B.Parallel
C.Proportional
D.Perpendicular
Easy
In ΔPQR, which angle is the 'included angle' between side PQ and side QR?
A.∠P
B.∠Q
C.∠R
D.There is no included angle.
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Frequently asked questions
What grade level is "Similarity rules for triangles"?
Similarity rules for triangles is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Similarity rules for triangles?
You'll be able to: Identify the pattern when dividing numbers by 10, 100, and 1,000 by recognizing how the decimal point shifts to the left; Solve division problems involving whole numbers and decimals divided by 10, 100, and 1,000 with at least….
Is "Similarity rules for triangles" free to practice?
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How many practice questions are included with Similarity rules for triangles?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.