IM Geometry Unit 3 4.3

Jade dilated triangle ABC using center P and scale factor 2.

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​4.3: Proof in Parallel

Multiple Choice

Jada claims that all the segments in ABC are parallel to the corresponding segments in A'B'C'. Her teacher asked her to write a conjecture. Which conjecture is Jada's?

• If a figure is dilated, then corresponding angles are congruent.

• Dilation takes lines to parallel lines.

• Dilating a line through the center of dilation will take all the points to points on that same line.

Draw

1. 1. Draw ray PC.

2. 2 Place a point E between point P and point C.

3. 3. Dilate point E by scale factor k=2 and label it E'

4. 4. Highlight the angles ECB and E'C'B'.

Reorder

Here is Jada's proof. Reorder the steps in the correct order.

• Mark a point E on ray BC.

• Dilate E and ray BC using center P and scale factor k.

• Points E' and C' will both be on ray PC by the definition of dilation

• Angle ECB is congruent to angle E'C'B' by the assertion "If a figure is dilated, then corresponding angles are congruent."

• Line  PC is a transversal for lines BC and B'C'. Corresponding angles are congruent therefore the lines must be parallel.

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• 2
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Drag and Drop

In Jada’s diagram the scale factor was greater than one. Would your proof have to change if the scale factor was less than one? ​

Placeholder

Drag these tiles and drop them in the correct blank above

Yes

No