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Unit 2 – Triangles

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temira
26 diapositives · 410 Views · Jul 27, 2014

This resource provides a comprehensive review of essential properties of triangles, including types of triangles, angle measures, and important theorems related to congruence and concurrency points. It covers true/false statements about scalene, isosceles, and obtuse triangles, as well as the incenter, centroid, and circumcenter. Students will also explore real-world applications like circumscribing circles and installing fixtures in triangular designs. Ideal for final exam preparation, it enhances understanding of triangle geometry and their properties.

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Unit 2 – Triangles
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  1. Unit 2 – Triangles Review for Final Exam

  2. True/False • A scalene triangle is a triangle with no two sides the same length.

  3. True/False • An obtuse triangle is a triangle that has one angle measuring greater than 90°.

  4. True/False • An isosceles right triangle is a triangle with an angle measuring 90° and no two sides congruent.

  5. True/False • If the base angles of an isosceles triangle each measure 48°, then the vertex angle has a measure of 132°.

  6. True/False • If a triangle has two angles of equal measure, then the triangle is equilateral.

  7. True/False • If a triangle has two angles of equal measure, then the third angle is acute.

  8. True/False • If two sides of a triangle measure 45 cm and 36 cm, then the third side must be greater than 9 cm and less than 81 cm.

  9. True/False • The sum of the measures of the three angles of an obtuse triangle is greater than the sum of the measures of the three angles of an acute triangle.

  10. True/False • The incenter, the centroid, and the circumcenterare always inside the triangle.

  11. True/False • An altitude of a triangle must be inside the triangle.

  12. True/False • The orthocenter of a triangle is the point of intersection of the three perpendicular bisectors of the sides.

  13. True/False • If is a median of and point D is the centroid, then TD = 3DR.

  14. True/False • The incenter of a triangle is the point of intersection of the three angle bisectors.

  15. Always/Sometimes/Never If a triangle is a right triangle, then the acute angles are complementary.

  16. Identify the point of concurrency. • A stained-glass artist wishes to circumscribe a circle about a triangle in her latest abstract design.

  17. Identify the point of concurrency. • Rosita wants to install a circular sink in her new triangular countertop. She wants to choose the largest sink that will fit.

  18. Identify the point of concurrency. • Julian Chive wishes to center a butcher-block table at a location equidistant from the refrigerator, stove, and sink.

  19. Identify the point of concurrency. • The first-aid center of Mt. Thermopolis State Park needs to be at a point that is equidistant from three bike paths that intersect to form a triangle.

  20. Determine the angle measures.

  21. Find x and y.

  22. Name the conjecture that leads to this congruence statement.