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Cogito

Integrated Math 1 · Chapter 7 · Lesson 3

Practice Worksheet

Coordinate Proof

Proving geometry with algebra.

12 problems · about 22 minutes · G-GPE.B.4

NameDate

Figure — use these to answer the problems

Place the figure with a vertex at the origin. Convenient placement is a choice, not a cheat.
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y = 0x + 4
Slope0
y-intercept4
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. A rectangle is 8 by 15. What is the diagonal length?

    Answer

  2. Why use letters rather than specific numbers in a coordinate proof?

    • One example does not prove a general statement.
    • Because letters are more rigorous to look at.

  3. To prove two sides equal, which tool? 1 distance, 2 slope, 3 midpoint.

    Answer

  4. To prove a segment is bisected, which tool? 1, 2 or 3?

    Answer

  5. To prove a right angle, which tool? 1, 2 or 3?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. A rectangle is 5 by 12. Diagonal length?

    Answer

  2. Midpoint of (0, 0) and (6, 8). x-coordinate?

    Answer

  3. Does proving it for one 3 by 4 rectangle prove it for all? 1 yes, 0 no.

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Match each claim with the tool that proves it.

    Draw a line from each item on the left to its match on the right.

    • Two sides have equal length
    • Two sides are parallel
    • A diagonal is bisected
    • Distance formula
    • Slope
    • Midpoint formula

  2. A rectangle is 9 by 12. Diagonal length?

    Answer

  3. The Diagonal

    A rectangle is 6 by 8. How long is each diagonal?

    Answer

  4. The Tool

    To prove two sides are parallel, which tool? 1 distance, 2 slope, 3 midpoint.

    Answer