Mathematics
Grade 9
15 min
Side lengths and angle measures of congruent figures (Set 1)
Side lengths and angle measures of congruent figures (Set 1)
What you'll learn
- Identify corresponding sides and corresponding angles in pairs of congruent figures.
- Determine the measure of an unknown side length in a congruent figure, given the corresponding side length in the original figure.
- Determine the measure of an unknown angle in a congruent figure, given the corresponding angle measure in the original figure.
- Explain why corresponding sides and corresponding angles of congruent figures are equal in measure.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define congruence in terms of rigid motions.
Identify corresponding sides and corresponding angles of congruent polygons.
Write a valid congruence statement for two polygons.
Use the definition of congruence to find the measures of unknown sides in congruent figures.
Use the definition of congruence to find the measures of unknown angles in congruent figures.
Apply the properties of congruent figures to solve multi-step algebraic problems.
Ever wonder how a company can make millions of identical phone cases that fit your phone perfectly? 📱 It's all about the geometry of congruent figures!
In this lesson, we'll explore congruent figures, which are exact copies of each other in size and shape. You will learn how to use a congruence statement to...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresTwo geometric figures are congruent if they have the exact same size and shape. This means one figure can be perfectly mapped onto the other using a sequence of rigid motions (translations, rotations, reflections).If you can trace Triangle A, then slide, turn, or flip the tracing paper to fit perfectly over Triangle B, then the two triangles are congruent.
Corresponding PartsThe matching sides and angles between two congruent figures. If two figures are congruent, all of their corresponding parts are also congruent.If △ABC ≅ △DEF, the corresponding parts are ∠A and ∠D, ∠B and ∠E, ∠C and ∠F, as well as sides AB and DE, BC and EF, and AC and DF.
Corresponding AnglesAngles that are in the same relative position in two congruent figures. They always have...
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Core Formulas
Corresponding Parts of Congruent Figures are Congruent (CPCFC)
If Polygon A ≅ Polygon B, then every corresponding part of Polygon A is congruent to its matching part in Polygon B.
This is the fundamental principle used to solve problems with congruent figures. Once you establish that two figures are congruent, you can set up equations by equating the measures of their corresponding sides and angles.
The Congruence Statement Rule
If `ABCDE ≅ PQRST`, then `∠A ≅ ∠P`, `∠B ≅ ∠Q`, etc., and `\overline{AB} ≅ \overline{PQ}`, `\overline{BC} ≅ \overline{QR}`, etc.
The order of the vertices in a congruence statement dictates the correspondence. The first vertex listed in the first figure corresponds to the first vertex in the second, the second to the second, and so on. This allows you...
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Challenging
Given △ABC ≅ △DEF, AB = x² - 1, and DE = 8. Which of the following is a possible value for x?
A.3
B.8
C.9
D.2
Challenging
Given that pentagon ABCDE ≅ pentagon PQRST. If m∠A = 100°, m∠B = (x + y)°, m∠Q = 120°, m∠C = (x - y)°, and m∠R = 80°, find the value of x.
A.80
B.120
C.100
D.20
Challenging
Given that △MNO ≅ △PQR, which of the following statements MUST be true?
A.△NOM ≅ △RQP
B.The altitude from N to MO is congruent to the altitude from P to QR.
C.△MNO is an isosceles triangle.
D.The median from M to NO is congruent to the median from P to QR.
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What grade level is "Side lengths and angle measures of congruent figures (Set 1)"?
Side lengths and angle measures of congruent figures (Set 1) is a Grade 9 Mathematics lesson on ExcelOS.
What will I learn in Side lengths and angle measures of congruent figures (Set 1)?
You'll be able to: Identify corresponding sides and corresponding angles in pairs of congruent figures; Determine the measure of an unknown side length in a congruent figure, given the corresponding side length in the original figure; Determine….
Is "Side lengths and angle measures of congruent figures (Set 1)" free to practice?
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How many practice questions are included with Side lengths and angle measures of congruent figures (Set 1)?
This lesson includes 23 practice questions across multiple difficulty levels, each with instant feedback and explanations.