# The Pythagorean Theorem

## TEACHING TIPS

SOLUTIONS

1. 48 sq. units
2. xy sq. units
3. 24 sq. units
4. 1/2xy sq. units.
5. a+a=2a
6. ab+ab=2ab
7. (1/2)a+(1/2)a = a
8. (1/2)ab+(1/2)ab=ab

SP2—Two Right Triangles
1. 3, 4
2. 4, 7
3. 9, 16
4. 16, 49
5. 25, 65
6.
7. In a right triangle, the area of the square on the hypotenuse is equal to the sum
of the areas of the squares on the two legs.

SP5—Right Triangle ABC

3. In a right triangle, the square of the length of the hypotenuse is equal to the
sum of the squares of the lengths of the legs.
4. Pythagorean theorem

SP6-7—Pythagorean Theorem Practice
1. 9 + 4 = 13; 32 + 22 = ( 13)2
2. 4 squared + 5 squared does not equal 9 squared. 16+25 does not equal
81.
3. 13
4. no
5. 3-4-5, 6-8-10

6. only the 6-8-10 triangle is a right triangle, by the converse to the Pythagorean
Theorem. The 4-6-8 triangle is not a right triangle, by the Pythagorean theorem.

7. This cannot be right because of the converse to the Pythagorean Theorem. The
given triangle is not a right triangle. Note: The Pythagorean Theorem itself does not
justify Tommy’s answer. The converse to the Pythagorean Theorem goes beyond
that, saying that Tommy’s answer also cannot be a lucky guess

 Prev Next