Practice on Finding Midpoints, Using the Pythagorean ...



Review on Midpoints, Distances, and the Pythagorean Theorem

Name________________________________________________period____________date_______

1. Given point A at -25 and point R at 32, find and show work

(a) the midpoint of segment AR

0

(b) the length of segment AR

2. Given point T (-16, 22) and point X (12, 10), find and show work (to graph let each space count 2)

(a) the midpoint of segment TX

(b) the length of segment TX

3. Given right triangle ABC find the missing side.

Show Work.

4. Given right triangle ABC find the length of side AC.

Show Work.

5. Given point M at 82 and point E at 26 find and show work

(a) the midpoint of segment ME

(b) the length of segment ME

6. Given point Y (12,-16) and point U (-14, 24) find and show work

(a) the midpoint of segment YU

(b) the length of segment YU

7. Make a sketch of right triangle DEF with angle E the right angle, side DE of length 23, and side FE with length 22. Find the length of the hypotenuse. Show Work.

8. Make a sketch of right triangle URA with angle R the right angle, side UR of length 17, and side UA of length 25. Find the length of side AR. Show work.

9. Given segment EZ with endpoint E (-2, -4) and midpoint (2,1). Find the other endpoint, Z.

10. (a) Plot quadrilateral TIGR on the coordinate system below.

T (-8,8) I (-5, -2) G(5,0) R(2,10)

(b) Find the following distances. Show work.

Length of segment TR

Length of segment RG

Length of segment GI

Length of segment IT

(c) Which if any of the above segments are equal?

What does this tell you about quadrilateral TIGR?

(d) Find the midpoint of each of the following segments and plot them on the graph below.

Show Work.

[pic] [pic] [pic] [pic]

[pic]

(e) Connect the midpoints in order that they were plotted. What shape do you see?

11. If the sides of a triangle are 5, 6, and 7, is the triangle a right triangle? Why?

12. If the sides of a triangle are 33, 44, and 55, is the triangle a right triangle? Why?

-----------------------

C

B

C

B

A

x

9

11

A

7

15

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