Question2: Which statement is true about the two triangles in the diagram?
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1 Question1: The diagram shows three aid stations in a national park. Choose the values of x, y, and z that COULD represent the distances between the stations. (a) x = 7 miles, y = 8 miles, z = 18 miles (b) x = 4 miles, y = 7 miles, z = 12 miles (c) x = 5 miles, y = 9 miles, z = 14 miles (d) x = 8 miles, y = 12 miles, z = 15 miles Question2: Which statement is true about the two triangles in the diagram? (a) The triangles are congruent, proven by ASA. (b) The triangles are congruent, proven by AAA. (c) The triangles are congruent, proven by HL. (d) The triangles are congruent, proven by SSA. 1
2 Question3: Which type of triangle has side lengths of 5 in, 6 in, and 7 in? (a) acute (b) equilateral (c) obtuse (d) right Question4: Two sides of a triangle measure 15 inches and 18 inches, respectively. Which of these is NOT a possible length for the third side of the triangle? (a) 4 inches (b) 18 inches (c) 32 inches (d) 36 inches Question 5: In South Carolina, the interstates of I-20, I-26 and I-95 approximately form a triangle. A warehouse is to be built that is equidistant from each of the three highways (incenter). Which construction on the triangle will identify the location for the warehouse? (a) medians (b) altitudes (c) angle bisectors (d) perpendicular bisectors Question 6: The three perpendicular bisectors of the sides of ΔABC intersect at point G. Point G is the (a) centroid (b) circumcenter (c) incenter (d) orthocenter 2
3 Question 7: The exterior angles of a triangle measure x + 3, 2x + 1, and 3x - 4. Find the measure of each exterior angle. (a) 18, 31, and 41 (b) 23, 41, and 56 (c) 33, 61, and 86 (d) 63, 121, and 176 Question 8: The diagonals of a are ALWAYS perpendicular. (a) parallelogram (b) quadrilateral (c) rectangle (d) rhombus Question 9: The diagram shows part of a regular polygon. Determine the number of sides for the polygon. (a) 8 (b) 9 (c) 10 (d) 11 Question 10: Which theorem proves that the triangles are congruent? (a) ASA (b) SAS (c) SSA (d) SSS 3
4 VOCABULARY SECTION: Write the correct terms next to each question 1. This is the point of concurrency of the medians of a triangle. This is also called the center of gravity. 2. If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent. 3. The sum of the lengths of two sides of a triangle is always greater than the length of the third side. (Example: In ΔABC, AB + BC > AC. ) 4. A convex polygon with congruent angles and congruent sides. 5. The point of concurrency of the angle bisectors of a triangle. 6. For a polygon, this is the angle formed inside a polygon by two adjacent sides. 7. This is the longest side of a right triangle only. It is also the side directly across from the 90-degree angle of a right triangle. (Example: 5 cm. in a 3 cm, 4 cm., 5 cm., right triangle.). ) 8. A quadrilateral with exactly two parallel sides. 9. If two sides and the included angle of one triangle are congruent to two sides and the included angle of a second triangle, then the two triangles are congruent Definition: The sides of a right triangle that form the right angle. 4
5 Notes Chapter 5: Geometry: Relationships in Triangles and Quadrilaterals 5
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