1201 Homework 8.5 3 December 1997

For this homework assignment you may use any theorem, postulate or definition we have discussed in class except the hypotenuse-leg theorem from homework 8 and the Pythagorean Postulate.

If you want to use any other theorems includes the proofs for them with your homework.

 

Definitions:

Rectangle–Any quadrilateral with four right angles.

Square–Any equal sided rectangle.

Area of a rectangle–The product of the lengths of two adjacent sides of the rectangle.

 

Postulate

Area Sum Postulate–The area of a closed figure formed by two non-overlapping closed figures is the sum of the areas of those two figures.

Question

In the figures below:

ABEF, CBHF, KJLF, MPSR, and WZXV are all squares.

Segments AC, EH, KJ, WP, ZS, RX, and MV are congruent. Use a to represent their length.

Segments CB, AK, LE, MW, PZ, SX, and VR are congruent. Use b to represent their length.

 

 

 

1. Prove that segments AJ, HL, VW, WZ, ZX, and XV are congruent. Call their length c.

2. Why is the area of a right triangle half of the product of the lengths of the legs of the right triangle?

3. Prove that (the area of CBHJ) + (the area of KJLF) = (the area of WZXV).

4. Write "(the area of CBHJ) + (the area of KJLF) = (the area of WZXV)" in terms of a, b and c.

5. Does the equation you wrote in #4 apply to all right triangles? Why?