A) Two triangles having corresponding sides congruent are necessarily congruent.

Transcription

1 1 Which of the following statements is FLS? ) Two triangles having corresponding sides congruent are necessarily congruent. ) Two triangles having three corresponding angles congruent are necessarily congruent. ) Two triangles having one congruent angle contained between two corresponding congruent sides are necessarily congruent. ) Triangle is congruent to triangle F and triangle F is congruent to triangle MN; therefore triangle is necessarily congruent to triangle MN. 2 Which of the four pairs of triangles below consists of two triangles that are definitely congruent? ) 4 cm ) 3 cm 3 cm cm 45 5 cm 45 5 cm ) ) 45 5 cm cm 10 cm cm 3 The following diagram shows lines,, F and GH In addition: G F // m LH = 75 m KJL = (3x) K? (2x) m LKJ = (2x) J (3x) L 75 H

2 ? 3x 4 In the figure, quadrilaterals and are parallelograms. What is the measure of angle? 65 2x 5 Louise wants to buy the piece of land corresponding to triangle shown in the rectangle. What is the area of this piece of land? 6 The mast of a sail is secured with two guy wires as shown in the adjacent figure. The angle formed at the point where the 2 guy wires are attached to the top of the mast is 90. The 1 st guy wire is attached to the deck 26 m from the foot of the mast. The 2 nd guy wire is attached 19 m from the foot of the mast at the opposite end of the deck. uring a storm, the 1 st guy wire broke. What length of cable is needed to replace it? 1 st guy wire mast 26 m 19 m 2 nd guy wire F 7 In the figure on the right, Lines and are parallel. Lines, and FG intersect at point I. Lines and FG intersect at point H. Which of the following statements allows you to state that angle FI is congruent to angle GH? I H G ) Vertically opposite angles are congruent. ) orresponding angles formed by two parallel lines and a transversal are congruent. ) lternate interior angles formed by two parallel lines and a transversal are congruent. ) lternate exterior angles formed by two parallel lines and a transversal are congruent.

3 ? 8 In the following figure: Lines and are parallel. Lines and intersect at point. 120 m = 120 m = The following is part of a procedure used to determine the measure of angle. omplete steps 1 and 2 of this procedure. Step 1 m + m = 180 m = 180 m = 60 because Step 2 m = m = 40 because Step 3 m + m + m = m = 180 m = 80 because the sum of the measures of the interior angles of a triangle is Isaac is building a house for his dog, Newton. His design is measured in decimetres. Triangle is isosceles and angles M, M and M each measures 90. What is the measure of each roof support, represented by 9 dm segments M and M? M 24 dm

4 10 In the adjacent circle with centre O, is perpendicular to at point O 13.5 cm m = 4 cm m O = 13.5 cm 4 cm What is the area of triangle? 11 In the adjacent figure, is the midpoint of segments and. rove that triangles and are congruent. Justify your statements. Statements Justifications 12 Triangle is inscribed in semicircle with centre O. is a diameter and. m = 17 cm m = 15 cm What is the area of the shaded region? O

5 m In a circus, a tightrope walker must able walk along two cables. The ends of able these cables are attached to anchor points. s indicated in the diagram, the Ground 15 m horizontal distance between anchor points and is 15 m. nchor point is located 3 m above the ground, and anchor point is located 2 m above the ground. nchor point, to which both cables are attached, is located at ground level. Line segments and represent the cables. nchor point is positioned so as to minimize the total combined length of the two cables. What is the total combined length of the two cables? Fred must make a sail in the shape of a right triangle for his boat by sewing together four different-coloured triangular pieces of canvas. 2 m Fred must use the measurements indicated on the following pattern. 6.4 m The pieces of canvas will be sewn together along 3 seams, which are represented on the pattern by segments, and. Fred wants the total length of seams and to be as short as possible. What is the minimum total length of seams and, in metres? 5.4 m 0.8 m 15 Triangle MNO has the following characteristics: m MNO = 35 m NMO = 45 m NO = 10 m Which one of the triangles below must be congruent to triangle MNO? ) ) m 100 ) m ) m 35

6 16 quilateral triangle is shown on the right. Line segments and have been drawn. oint is a point on segment. oint is a point on segment In addition, segments and are congruent. The following is part of a procedure used to show that segments and are congruent. omplete steps 4 and 5 of this procedure. In triangles and : Step 1 because in an equilateral triangle, each of the interior angles measures 60. Step 2 Step 3 because the 3 sides of an equilateral triangle are equal in length. by hypothesis Step 4 because... Step 5 because...