Exam 9: Geometry

Decide whether the statement is true or false. -A figure is said to be convex if, for any two points A and B inside the figure, the line segment AB is at least partially outside the figure.

There are various formulas that will generate Pythagorean triples. Use the specified formula and specified values to generate a Pythagorean triple. -For positive integers $r$ and $s$ such that $r > s$ , the following set of equations will generate $a$ Pythagorean triple $( a , b , c )$ . $a = r ^ { 2 } - s ^ { 2 } , b = 2 r s , c = r ^ { 2 } + s ^ { 2 } \text {. }$ Use this method with the values $\mathrm { r } = 8$ and $\mathrm { s } = 1$ to generate a Pythagorean triple.

Solve the problem. -In order to measure the distance across a pond (from A to B), Yuko made some measurements, which are given below the drawing. What is the distance (to the nearest unit)? $\angle \mathrm { ABE } = 55 ^ { \circ } , \mathrm { BE } = 168 \mathrm { ft } , \mathrm { ED } = 48 \mathrm { ft } , \mathrm { DC } = 43 \mathrm { ft } , \mathrm { CE } = 51 \mathrm { ft } , \angle \mathrm { DCE } = 55 ^ { \circ }$

Find the measure of each unknown angle in triangle ABC. - $\angle \mathrm { A } = ( 40 \mathrm { x } - 17 ) ^ { \circ } , \angle \mathrm { B } = ( 35 - 2 \mathrm { x } ) ^ { \circ } , \angle \mathrm { C } = ( 6 + \mathrm { x } ) ^ { \circ }$

Match the symbol with the answer choice that names the same set of points based on the given figure. -

There are various formulas that will generate Pythagorean triples. Use the specified formula and specified values to generate a Pythagorean triple. -For any integer n greater than 1, $\left( 2 n , n ^ { 2 } - 1 , n ^ { 2 } + 1 \right)$ is a Pythagorean triple . Use this method with the value $\mathrm { n } = 8$ to generate a Pythagorean triple.

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $\text { Line segment } \mathrm{QR}$

Solve the problem. - Find the area.

Match the symbol with the answer choice that names the same set of points based on the given figure. -

a and b represent the two legs of a right triangle, while c represents the hypotenuse. Find the length of the unknown side. - $\mathrm { a } = 20 \mathrm { ft } , \mathrm { c } = 52 \mathrm { ft }$

Find the area. - (a trapezoid)

There is no angle that is the complement of an obtuse angle.

For the given pair of similar triangles, name the corresponding side or angle in the other triangle. -

The two triangles below are similar. Find the unknown side lengths. - $\triangle C A B$ is similar to $\triangle C S R$ Given that $S C = 60 , A S = 75 , C R = 68$ , find $C B$ .

The two triangles below are similar. Find the unknown side lengths. -

Find the area. - $a = 30 \mathrm {~m} , \mathrm {~b} = 90 \mathrm {~m}$

Find the measure of the angles. -

Identify the curve as simple, closed, both, or neither. -

Find the requested angle. -Supplement of 72°

Give the symbol that represents the portion of the line named and draw a figure showing just the portion named. - $\text { Line segment RP }$