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Lesson 2.1 Congruent Figures
Name corresponding angles and corresponding sides of congruent figures; identify congruent figures (CC.SS.8.G.2)
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Warm-Up Given 3x + y = 3, if y = 3 find the value of x
4x + 2x – 2 = 42 solve for x Find the volume of a cylinder if the diameter is 4 inches.
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Transformation – a change in the ___________, _________ , or _________ of a figure.
Rigid Transformation – a change in the position of a figure that does not change its _______________ or ________________. Pre-image – the __________ figure in a transformation. Image – the _____________ figure (new) in a transformation. Isometry – a transformation in which the original figure and its image are ___________. Prime – a notation to identify new images being created. It looks like this: A’ or A’’ or A’’’ or A’’’’ size shape position size shape original resulting congruent
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Transformations on the Coordinate Plane
Algebra 4-2 Transformations on the Coordinate Plane Transformations on the Coordinate Plane Line of reflection NOT A RIGID TRANSFOMRATION NOT AN ISOMETRY Transformations on the Coordinate Plane Harbour
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Transformations Notation
A transformation transforms, or maps, the original point to another point. Transformation uses a combination of operations (+, −, ÷, x) notation: ↦ “maps to” (it is a rule that you have to apply) Example: (x, y) ↦ (x+3, y) RULE (5, 12) ↦ (5+3, 12) ( 8, 12) new point
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Problem 1: (3, -2) (4, 1) (-5, -2) (-7, 0) a) (x, y) ↦ (x, y - 2 )
(3, -2) (4, 1) (-5, -2) (-7, 0) a) (x, y) ↦ (x, y - 2 ) b) (x, y) ↦ (x - 3, y) c) (x, y) ↦ (2x, y + 2 ) (3,-4) (4,-1) (-5,-4), (-7,-2) (0,-2) (1,1) (-8,-2) (-10,0) (6,0) (8,3) (-10,0) (-14,2)
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How can you identify congruent triangles?
Two figures are congruent when they have the same size and the same shape.
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Congruent shapes
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Transformation Translation (slide), Reflection (mirror), Rotation (turn) maintain the congruency of the shapes. Dilation (enlarge/reduce) does not maintain the congruency of the shapes.
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Congruent: YES? No?
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Yes or no?
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Yes or no?
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Yes or no?
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Yes or no?
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More Flips
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Identifying Congruent Figures
Two figures are congruent when corresponding angles and corresponding sides are congruent. Triangle ABC is congruent to Triangle DEF.
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Problem 2: The figures are congruent
Problem 2: The figures are congruent. Name the corresponding angles and the corresponding sides.
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Problem 3 32 ft ∡𝑀 20 ft 96 ft
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Problem 4
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