Exam 6: Geometry

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Explain why the indicated triangles are congruent. - NK=LK.NKMLKM\mathrm{NK}=\mathrm{LK} . \quad \triangle \mathrm{NKM} \cong \triangle \mathrm{LKM} . Explain how you know that NM=LM\mathrm{NM}=\mathrm{LM} .  Explain why the indicated triangles are congruent. - \mathrm{NK}=\mathrm{LK} . \quad \triangle \mathrm{NKM} \cong \triangle \mathrm{LKM} . Explain how you know that  \mathrm{NM}=\mathrm{LM} .

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Since NK=LK,KNKL\mathrm{NK}=\mathrm{LK}, \overline{\mathrm{KN}} \cong \overline{\mathrm{KL}} . NKMLKM\triangle \mathrm{NKM} \cong \triangle \mathrm{LKM} is given. KMKM\overline{\mathrm{KM}} \cong \overline{\mathrm{KM}} . So two sides and an included angle of KKM\triangle \mathrm{KKM} are congruent to the corresponding parts of NKM\triangle \mathrm{NKM} . So LKMΔNKM\triangle \mathrm{LKM} \cong \Delta \mathrm{NKM} by SAS. Since LKMΔNKM,NMLM\triangle \mathrm{LKM} \cong \Delta \mathrm{NKM}, \overline{\mathrm{NM}} \cong \overline{\mathrm{LM}} and therefore NM=LM\mathrm{NM}=\mathrm{LM} .

Find the radius or diameter as requested. -Find the radius. Find the radius or diameter as requested. -Find the radius.

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B

Solve the problem. -A room measures 14ft14 \mathrm{ft} by 20ft20 \mathrm{ft} . The ceiling is 12ft12 \mathrm{ft} above the floor. The door is 3ft3 \mathrm{ft} by 7ft7 \mathrm{ft} . A gallon of paint will cover 84.2ft284.2 \mathrm{ft}^{2} . How many gallons of paint are needed to paint the room (including the ceiling and not including the door). Round your answer up to the next whole number.

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A

Determine whether the pair of triangles is congruent by the ASA property. -Determine whether the pair of triangles is congruent by the ASA property. -

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Find the area. -Find the area. -

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Solve the problem. Use 3.14 for π\pi . -Find the cost to asphalt a circular racetrack if asphalt costs $60\$ 60 per 100ft2100 \mathrm{ft}^{2} . (Round to the nearest dollar.) =75 =95  Solve the problem. Use 3.14 for  \pi . -Find the cost to asphalt a circular racetrack if asphalt costs  \$ 60  per  100 \mathrm{ft}^{2} . (Round to the nearest dollar.)  \begin{aligned} & \mathrm{r}=75 \mathrm{ft} \\ & \mathrm{R}=95 \mathrm{ft} \end{aligned}

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Find the area. -Find the area of a square measuring 15.1 m15.1 \mathrm{~m} on a side.

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Find the area of the figure. Use 3.14 for π\pi . - Find the area of the figure. Use 3.14 for  \pi . -

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Solve the problem. -Find the total area of the ends of the garage. Solve the problem. -Find the total area of the ends of the garage.

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Find the area of the figure. Use 3.14 for π\pi . - Find the area of the figure. Use 3.14 for  \pi . -

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Provide an appropriate response. -For the pair of similar triangles, name the congruent angles and proportional sides. ABCZML\triangle \mathrm{ABC} \sim \triangle \mathrm{ZML}

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Determine whether the pair of triangles is congruent by the ASA property. -Determine whether the pair of triangles is congruent by the ASA property. -

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Find the sum of the angle measures of the specified polygon. -A dodecagon.

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Find the area. -Find the area. -

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Solve the problem. Use 3.14 for π\pi . Round to the nearest tenth. -A toy baseball bat comes with 3 plastic balls in a box that is a rectangular solid. The box is just big enough to hold the 3 balls. The radius of the balls is 1.4in1.4 \mathrm{in} . What is the volume of the air in the box surrounding the balls.

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Find the area. -Find the area of a square measuring 6236 \frac{2}{3} in. on a side.

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Classify the polygon by name. -Classify the polygon by name. -

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Solve the problem. -Find the height of the building. Assume that the height of the person is 5ft5 \mathrm{ft} .  Solve the problem. -Find the height of the building. Assume that the height of the person is  5 \mathrm{ft} .

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Provide an appropriate response. -For the pair of similar triangles, name the corresponding sides and angles. Provide an appropriate response. -For the pair of similar triangles, name the corresponding sides and angles.

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Find the volume. -Find the volume of a box 15ft×19ft×22ft15 \mathrm{ft} \times 19 \mathrm{ft} \times 22 \mathrm{ft} .

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