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Geometry Fundamentals

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Geometry Fundamentals

Use angle relationships, triangle properties, circle vocabulary, and coordinate geometry to check a proposed skate-park layout. Show calculations and include units where appropriate.

Angles in the Park

The entrance path crosses a straight boundary line. At the intersection, one angle measures 68°.

1.The angle opposite the 68° angle is formed by the same two intersecting lines. What is its measure, and what angle relationship justifies your answer?
2.The angle next to the 68° angle lies on the same straight boundary line. Find its measure and name the relationship between the two angles.
3.A ramp makes a 37° angle with level ground. What angle would complete a complementary pair with this angle?

Triangular Features

A triangular planter has two interior angles measuring 48° and 67°.

4.Calculate the third interior angle of the planter. Show how the Triangle Sum Theorem helps.
5.A support frame has side lengths 5 ft, 5 ft, and 8 ft. Classify it by its sides, and explain your choice.
6.Two proposed triangular braces have side lengths 6 ft, 8 ft, and 10 ft each. Is SSS enough to prove the triangles congruent? Choose the best answer.
  • Yes; three pairs of equal corresponding sides prove congruence.
  • No; only angles can prove triangles congruent.
  • No; SSA always proves congruence, but SSS does not.
  • Yes; any one equal side is enough.

Circle and Coordinate Check

Use the circle information given in Question 7 to answer that question.

7.A circle has center O. Segment OA goes from the center to point A on the circle. Segment BC passes through O, with B and C on the circle. Segment DE joins two points D and E on the circle without passing through O. A line touches the circle at T only. Match each segment or line to its name.
  • 1. O to A
  • 2. B to C
  • 3. D to E
  • 4. Line at T
  • D. Diameter
  • A. Chord
  • B. Tangent
  • C. Radius
8.A circular practice area has a radius of 9 ft. What is its diameter?
9.On a coordinate grid, two corners of a rectangular platform are P(−2, 1) and Q(4, 9), opposite each other. Find the diagonal length PQ. Give an exact answer and a decimal to the nearest tenth.
10.The layout team says a line is tangent to a circular feature because it touches the circle at exactly one point. Is that definition correct? Explain briefly.

3 printable pages

  • Geometry Fundamentals, page 1 of 3: Angles in the Park, Triangular Features

    Page 1

  • Geometry Fundamentals, page 2 of 3: Circle and Coordinate Check

    Page 2

  • Geometry Fundamentals, page 3 of 3: 10. The layout team says a line is tangent to a circular feature because it touches the…

    Page 3

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