8th Grade Unit 6
Name
Distance, mid-point, and coordinate proof Study Guide
Date
Period:
Can you Use the Pythagorean Theorem?
1. Determine whether each set of numbers can be measures of the sides of a triangle. If so, classify the
triangle as acute, obtuse, or right. Justify your answer.
a.
7, 24, 25
b.
20, 21, 29
c.
2. The bottom end of a ramp at a warehouse
is 10 m from the base of the main dock and
11 m long. How high is the dock?
3.
3 2, 7, 4
A 50-foot-long cable is tied to a pole at
s point 40 feet above the ground. The
cable is fastened to an anchor in the
ground. How far way from the base of
the pole is the anchor?
Can you calculate distance on a coordinate grid using the distance formula?
4. Find the distance between the points (2, 3) and (-1, -4).
Can you calculate the midpoint on a coordinate grid using the midpoint formula?
5a. Find the midpoint between the points
(2, 3) and (-1, -4).
5b. If C(-5, 7) is the midpoint of segment AB
and A(8, 15), find the coordinates of B.
Can you use slope, mid-point, and distance formulas in coordinate proofs?
6. If AB = 90 AD = 8 and, determine
whether ABCD below is a parallelogram.
7.
Prove or disprove that the triangle with
vertices R(-2, -2), S(1, 4), and T(4, -5)
is an equilateral triangle.
7. ΔABC has vertices A(−4, 1), B(−3, 4), and C(−1, 1). ΔDEF has vertices D(2, −3), E(5, −2), and F(2,
0). Prove or disprove that the triangles are congruent.
8. Prove or disprove that the quadrilateral formed by A(-2, 3) B(5, 3) C(3, -1) and D(-3, -1) is a
parallelogram.
9. Suppose you wish to prove that the mid-point of the hypotenuse of a right triangle is the same
distance from each of its three vertices. Draw the right triangle on a coordinate grid so that it
represents all right triangles. Be strategic on where you locate the triangle. Complete the proof.