Mathematics
Grade 10
15 min
Side lengths and angle measures in similar figures
Side lengths and angle measures in similar figures
What you'll learn
- Solve division word problems involving multi-digit numbers divided by 1-digit numbers with 80% accuracy.
- Explain the steps used to solve a division word problem with multi-digit numbers divided by 1-digit numbers in a complete sentence.
- Identify the dividend, divisor, and quotient in a division word problem at least 4 out of 5 times.
- Apply the division algorithm to solve real-world problems involving equal sharing and grouping with multi-digit numbers divided by 1-digit numbers.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define geometric similarity and correctly identify corresponding angles and sides.
State the two core properties of similar figures: corresponding angles are congruent and corresponding side lengths are proportional.
Set up and solve proportions to find unknown side lengths in similar polygons.
Calculate and apply a scale factor to determine missing side lengths.
Determine an unknown angle measure in a similar figure by identifying its corresponding congruent angle.
Verify if two polygons are similar by systematically checking their angles and side length ratios.
How can a cartographer fit the entire country on a small map while keeping all the state shapes correct? 🗺️ It's all about the geometry of similarity!
This tutorial explores the fundamental...
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Key Concepts & Vocabulary
TermDefinitionExample
Similar FiguresTwo geometric figures that have the exact same shape but can be different sizes. One is an enlargement or reduction of the other.A 4x6 inch photograph and an 8x12 inch photograph of the same image are similar figures.
Corresponding AnglesAngles that are in the same relative position in two similar figures. In similar figures, corresponding angles are always congruent (equal in measure).If $\triangle ABC \sim \triangle XYZ$, then $\angle A$ corresponds to $\angle X$, and their measures are equal.
Corresponding SidesSides that are in the same relative position in two similar figures. The lengths of corresponding sides are proportional.If quadrilateral $PQRS \sim$ quadrilateral $TUVW$, then side $PQ$ corresponds to side $TU$.
ProportionAn equation that st...
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Core Formulas
Angle Congruence in Similar Figures
If two figures are similar, their corresponding angles are congruent (equal in measure).
This is a straightforward rule. If you know two polygons are similar, you can directly transfer the measure of an angle to its corresponding angle in the other figure. No calculation is needed. For example, if $\triangle ABC \sim \triangle DEF$, then $m\angle A = m\angle D$, $m\angle B = m\angle E$, and $m\angle C = m\angle F$.
Side Proportionality in Similar Figures
If two figures are similar, the ratio of the lengths of their corresponding sides is constant. This constant ratio is the scale factor, $k$. If $\triangle ABC \sim \triangle DEF$, then $\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF} = k$.
This is the core formula for finding unknown side le...
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Challenging
Triangle ABC has vertices A(0,0), B(4,0), and C(2,3). Triangle DEF has vertices D(0,0), E(8,0), and F(4,6). What is the scale factor from ΔABC to ΔDEF?
A.1/2
B.2
C.3
D.4
Challenging
In the figure provided, ∠ABC and ∠ADE are right angles. If AB=12, BC=9, and AD=8, what is the length of DE?
A.6
B.7.5
C.5.33
D.4
Challenging
You are given two triangles, ΔJKL and ΔMNO, with JK/MN = KL/NO. Which single piece of additional information would be sufficient to prove that ΔJKL ~ ΔMNO?
A.m∠J = m∠M
B.JL = MO
C.m∠L = m∠O
D.m∠K = m∠N
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Frequently asked questions
What grade level is "Side lengths and angle measures in similar figures"?
Side lengths and angle measures in similar figures is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Side lengths and angle measures in similar figures?
You'll be able to: Solve division word problems involving multi-digit numbers divided by 1-digit numbers with 80% accuracy; Explain the steps used to solve a division word problem with multi-digit numbers divided by 1-digit numbers in a complete….
Is "Side lengths and angle measures in similar figures" free to practice?
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How many practice questions are included with Side lengths and angle measures in similar figures?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.