The endpoints of DE are D(-4,11) and E(-4,-13). The endpoints of GH are G(-14,5) and H(-9,5). Are DE and GH congruent? Explain.
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Answer:
Step-by-step explanation:
Since this is a right triangle, we can use the Pythagorean Theorem to solve for the sides.
where <em>a</em> and<em> b</em> are the legs and <em>c</em> is the hypotenuse. In this triangle, we know the legs are 9 centimeters and 11 centimeters, or:
- a= 9 cm
- b= 11 cm
Substitute these values into the formula.
Solve the exponents.
- (9 cm)²= 9 cm*9 cm=81 cm²
- (11 cm)²= 11 cm*11 cm= 121 cm²
Add the values on the left side.
Since we are solving for c, we must isolate the variable. It is being squared and the inverse of a square is the square root. Take the square root of both sides.
We are told to round to the nearest tenth.
- 14.2<u>1</u>26704036
The 1 in the hundredth place tells us to leave the 2 in the tenth place.
The hypotenuse is equal to <u>14.2 centimeters.</u>