Corresponding Parts and Scale Factors

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To Investigating Corresponding Parts and Scale Factor.

A road sign for railroad crossings is a circle with a large X in the middle and two R’s. Here below is a picture with some points labeled and two copies of the picture.

  • Drag the elements in the rectangular boxes and place them as corresponding parts in the three pictures.​

(1). Use the moveable angle tool to compare angle KLM with its corresponding angles in Copy 1 and Copy 2.

(2). What do you notice?

(3). Use the moveable angle tool to compare angle NOP with its corresponding angles in Copy 1 and Copy 2.

(4). What do you notice?

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To Identify Scaled Copies of a Triangle.

In the figure below is Triangle O, followed by a number of other triangles.

(1). Which of the triangles is a scaled copy of Triangle O? Explain your reasoning for choosing each triangle.

(2). List all the triangles that are scaled copies in the table. Record the side lengths that correspond to the side lengths of Triangle O listed in each column.

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To Identify Corresponding points and Corresponding sides.

The second H-shaped polygon is a scaled copy of the first. Show one pair of corresponding points and two pairs of corresponding sides in the original polygon and its copy. Consider labeling corresponding parts or some of the vertices.

What scale factor takes the original polygon to its smaller copy? Explain or show your reasoning.

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Polygon B is a scaled copy of Polygon A.

(1). What is the scale factor from Polygon A to Polygon B? Explain your reasoning.

(2). Find the missing length of each side marked with ? in Polygon B.

(3). Determine the measure of each angle marked with ? in Polygon A.

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(1). These triangles are scaled copies of each other. What is the scale factor?

(2). These rectangles are scaled copies of each other. What is the scale factor?

(3). These rectangles are scaled copies of each other. What is the scale factor from ABCD to UVWX?

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