Chapter 3 Review
Textbook
10 Math Workbook
Chapter
Chapter 3
Section
Chapter 3 Review
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Solutions 16 Videos

a) Define the right bisector of a side of a triangle.

b) List three additional properties of the right bisectors of the sides of a triangle.

c) Outline how you could use geometry software to show that the right bisectors of the sides of all triangles have these properties.

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Q1

a) Show that two of the medians of an isosceles triangle are equal in length.

b) Show that the median from the vertex between the equal sides in an isosceles triangle is also an altitude of the isosceles triangle.

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Q2

a) Which type of triangle has at least one median that is also an altitude?

b) Which type of triangle has more than one median that is also an altitude and an angle bisector of the vertex?

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Q3

a) Verify that the triangle with vertices P(-3, 2), Q(2, 5), and R(2, -1) is an isosceles triangle.

b) Find the midpoint, M, of the side PR and the midpoint, N, of the side PQ.

c) Verify that the lengths of the medians of the two equal sides of the isosceles triangle are equal.

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Q4

a) Classify \triangle DEF. Explain your reasoning.

b) Verify that the median from vertex E bisects \angle DEF in \triangle DEF.

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Q5

a) Verify that \triangle ABC is a right triangle.

b) Describe another method that you could use to verify that \triangle ABC is a right triangle.

c) Verify that the midpoint, M, of the hypotenuse of \triangle ABC is equidistant from all three vertices.

d) Determine the area of \triangle ABC.

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Q6

List two properties of the diagonals of each of these geometric shapes.

a) rectangle

b) rhombus

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Q7

a) Identify each of the quadrilaterals.

b) List two properties of the diagonals of each geometric shape in part a).

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Q8

a) Draw any kite ABCD.

b) Identify the longer diagonal in kite ABCD.

c) Show that the longer diagonal of kite ABCD bisects the area of the kite. Explain your reasoning.

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Q9

Verify that quadrilateral JKLM is a parallelogram.

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Q10

a) Draw any trapezoid QRST.

b) Find the midpoints, M and N, of the non-parallel sides of the trapezoid.

c) Show that the line segment joining M and N is parallel to the two parallel sides in the trapezoid.

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Q11

Use geometry software to answer question 11. Outline your method.

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Q12

a) Draw the quadrilateral with vertices W(-2, 2),X(1, 3), Y(5, 0), and Z(-4, -3).

b) Classify the quadrilateral WXYZ. Justify this classification.

c) Verify that the line segment joining the midpoints of the non-parallel sides of WXYZ is parallel to the parallel sides of the quadrilateral.

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Q13

a) Verify that A(-24, 7) and B(24, -7) are endpoints of a diameter of the circle x^2 + y^2 = 625.

b) State the coordinates of another point with integer coordinates, C, on the circle x^2 + y^2 = 625.

c) Verify that \triangle ABC is a right triangle.

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Q14

a) Verify that the points J(-6, 3) and K(3, -6) lie on the circle with equation x^2 + y^2 = 45.

b) Verify that the right bisector of the chord JK passes through the centre of the circle.

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Q15

Three friends live in different areas of the same city. They are planning to go to a restaurant for dinner to celebrate a birthday.

a) Describe how the friends could use a city map to find a suitable restaurant.

b) What factors might prevent that restaurant from being the one they select for their dinner?

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Q16