Mathematics
Grade 10
15 min
Identify congruent figures
Identify congruent figures
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1
Introduction & Learning Objectives
Learning Objectives
Define congruence in terms of rigid motions.
Identify all corresponding angles and corresponding sides of congruent polygons.
Write a correct congruence statement for two congruent polygons, ensuring the order of vertices is accurate.
Use the definition of congruence to find the measure of unknown sides and angles in a figure.
Verify if two figures on a coordinate plane are congruent by comparing their corresponding side lengths and angles.
Distinguish between congruent figures (same size and shape) and similar figures (same shape, different size).
Ever wonder how a factory can produce millions of identical phone parts or car doors? ⚙️ They rely on the mathematical principle of congruence!
In this lesson, you'll learn the precise definition of congr...
2
Key Concepts & Vocabulary
TermDefinitionExample
Congruent FiguresTwo or more geometric figures that have the exact same size and shape. One figure can be perfectly superimposed on the other using a sequence of rigid motions.Two 5-inch by 7-inch rectangular photos are congruent. A 5x7 photo and an 8x10 photo are not congruent.
Corresponding PartsThe sides and angles that are in the same relative position in two congruent figures. If two figures are congruent, all their corresponding parts are also congruent.If ΔABC ≅ ΔDEF, then side AB corresponds to side DE, and angle ∠C corresponds to angle ∠F.
Rigid Motion (Isometry)A transformation that preserves distance, angle measure, and overall size. It moves a figure without changing its shape. The three types are translations (slides), rotations (turns), and reflections...
3
Core Formulas
Definition of Congruent Polygons
Two polygons are congruent if and only if all of their corresponding parts (sides and angles) are congruent. For triangles, `ΔABC ≅ ΔDEF` if and only if: `∠A ≅ ∠D`, `∠B ≅ ∠E`, `∠C ≅ ∠F` and `AB ≅ DE`, `BC ≅ EF`, `AC ≅ DF`.
This is the fundamental test for congruence. To prove two polygons are congruent, you must show that every corresponding side and every corresponding angle is congruent.
Rigid Motion Principle of Congruence
Two figures, `F_1` and `F_2`, are congruent if and only if there exists a sequence of one or more rigid motions (translation, rotation, reflection) that maps `F_1` exactly onto `F_2`.
This rule provides a transformational perspective on congruence. If you can slide, turn, and/or flip a figure to land perfectly on another...
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Sign Up Free to ContinueSample Practice Questions
Easy
According to the definition provided, what must be true for two geometric figures to be considered congruent?
A.They must have the same orientation and position.
B.They must have the same area but can have different shapes.
C.They must have the exact same size and shape.
D.They must have the same number of sides and angles.
Easy
If it is given that quadrilateral ABCD ≅ quadrilateral EFGH, which of the following statements about their corresponding angles must be true?
A.∠A ≅ ∠E, ∠B ≅ ∠F, ∠C ≅ ∠G, ∠D ≅ ∠H
B.∠A ≅ ∠H, ∠B ≅ ∠G, ∠C ≅ ∠F, ∠D ≅ ∠E
C.∠A ≅ ∠F, ∠B ≅ ∠E, ∠C ≅ ∠H, ∠D ≅ ∠G
D.∠A ≅ ∠B, ∠C ≅ ∠D, ∠E ≅ ∠F, ∠G ≅ ∠H
Easy
Given the congruence statement ΔPQR ≅ ΔSTU, which side corresponds to side TU?
A.PQ
B.QR
C.RP
D.ST
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