Lesson 2.1 Congruent Figures

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Presentation transcript:

Lesson 2.1 Congruent Figures Name corresponding angles and corresponding sides of congruent figures; identify congruent figures (CC.SS.8.G.2)

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.

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

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

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

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)

How can you identify congruent triangles? Two figures are congruent when they have the same size and the same shape.

Congruent shapes

Transformation Translation (slide), Reflection (mirror), Rotation (turn) maintain the congruency of the shapes. Dilation (enlarge/reduce) does not maintain the congruency of the shapes.

Congruent: YES? No?

Yes or no?

Yes or no?

Yes or no?

Yes or no?

More Flips

Identifying Congruent Figures Two figures are congruent when corresponding angles and corresponding sides are congruent. Triangle ABC is congruent to Triangle DEF.

Problem 2: The figures are congruent Problem 2: The figures are congruent. Name the corresponding angles and the corresponding sides.

Problem 3 32 ft ∡𝑀 20 ft 96 ft

Problem 4