Mathematics
Grade 10
15 min
Solve problems involving corresponding parts
Solve problems involving corresponding parts
What you'll learn
- Identify the numerator and denominator in a fraction with 100% accuracy.
- Solve addition problems involving two fractions with like denominators and express the answer in simplest form in at least 8 out of 10 attempts.
- Solve subtraction problems involving two fractions with like denominators and express the answer in simplest form in at least 8 out of 10 attempts.
- Explain, using words or pictures, why we can only add or subtract fractions when they have the same denominator.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Identify corresponding angles and sides of congruent polygons given a congruence statement.
Write a valid congruence statement for two congruent polygons by matching vertices correctly.
Use the definition of congruence to find unknown angle measures in congruent figures.
Apply the concept of corresponding parts to determine unknown side lengths in congruent figures.
Set up and solve single-variable and multi-step algebraic equations based on the equality of corresponding parts.
Justify conclusions in geometric problems using the principle that Corresponding Parts of Congruent Figures are Congruent (CPCTC).
How do manufacturers ensure every single part, from a phone screen to a car door, fits perfectly every time? ⚙️ The secret lies in the geometry of cong...
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Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresTwo or more geometric figures that have the exact same size and shape. One figure can be perfectly mapped onto the other through a sequence of rigid motions (translations, rotations, reflections).If you can place one triangle directly on top of another so that all vertices and sides match up perfectly, then \(\Delta ABC \) and \(\Delta DEF \) are congruent.
Corresponding PartsThe specific sides and angles in congruent figures that are in the same position and match up with each other.If \(\Delta ABC \cong \Delta DEF \), then \(\angle A\) corresponds to \(\angle D\), and side \(BC\) corresponds to side \(EF\).
Congruence StatementA formal statement declaring that two figures are congruent. The order of the vertices in the statement is critical as it d...
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Core Formulas
Definition of Congruent Polygons
Two polygons are congruent if and only if all of their corresponding parts (sides and angles) are congruent.
This is the foundational principle. If you are given that two figures are congruent, you can assume every matching part is also congruent. This allows you to set their measures equal to each other.
Congruence Statement Implication
If Polygon \(ABCDE \cong\) Polygon \(PQRST\), then: \(\angle A \cong \angle P, \angle B \cong \angle Q, ...\) and \(\overline{AB} \cong \overline{PQ}, \overline{BC} \cong \overline{QR}, ...\)
The order of the vertices in a congruence statement is a map. The first vertex listed on the left corresponds to the first on the right, the second to the second, and so on for all vertices, sides, and angles.
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Challenging
Given ΔABC ≅ ΔXYZ. The perimeter of ΔABC is 60 cm. If XY = 2x + 3, YZ = 3x - 1, and ZX = x + 4, what is the length of the longest side of ΔXYZ?
A.9 cm
B.21 cm
C.13 cm
D.26 cm
Challenging
In the given figure, ΔABD is congruent to ΔCBD, and point D is not on the line segment AC. If m∠ADB = 80° and m∠DAB = 45°, what is the measure of ∠ADC?
A.90°
B.125°
C.160°
D.135°
Challenging
You are given that ΔABC ≅ ΔDEF and ΔDEF ≅ ΔGHI. If m∠A = (5x - 10)° and m∠G = (3x + 20)°, what is the measure of ∠D?
A.65°
B.15°
C.75°
D.85°
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What grade level is "Solve problems involving corresponding parts"?
Solve problems involving corresponding parts is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Solve problems involving corresponding parts?
You'll be able to: Identify the numerator and denominator in a fraction with 100% accuracy; Solve addition problems involving two fractions with like denominators and express the answer in simplest form in at least 8 out of 10 attempts; Solve….
Is "Solve problems involving corresponding parts" free to practice?
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How many practice questions are included with Solve problems involving corresponding parts?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.