Chapter

Chapter 3
Section

Practice Test Geometric Test

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Solutions
13 Videos

Which of these triangles have at least two medians that are equal in length? Justify your choices.

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Q1

Which of the triangles have a median that is also an altitude? Justify your choices.

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Q2

Sketch an example of each of these types of quadrilateral. Show the diagonals on each sketch and indicate whether they are equal in length and whether they bisect each other.

**a)** square

**b)** rectangle

**c)** parallelogram

**d)** rhombus

**e)** trapezoid

**f)** quadrilateral with no equal sides

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Q3

Show that two of the altitudes of an isosceles triangle are equal in length.

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Q4

**a)** Verify that `\triangle ABC`

is isosceles.

**b)** Verify that the centroid of `\triangle ABC`

lies at `(6, -1)`

.

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Q5

**a)** Show that the triangle with vertices `D(-2, 5), E(-4, 1),`

and `F(2, 3)`

is a right triangle.

**b)** Verify that the midpoint of the hypotenuse of `\triangle DEF`

is equidistant from all three vertices.

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Q6

Use analytic geometry to verify that quadrilateral `JKLM`

is a rhombus.

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Q7

**a)** Find the midpoint of each side of the quadrilateral with vertices `P(-3, 8), Q(1, 10), R(5, 6),`

and `S(7, -4)`

.

**b)** Show that joining the midpoints of the adjacent sides of `PQRS`

forms a parallelogram.

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Q8

**a)** Verify that `C(5, 2)`

is the centre of the circle that passes through points `T(5, 15), U(17, -3),`

and `V(-8, 2)`

.

**b)** Find the radius of the circle.

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Q9

Verify that quadrilateral `ABCD`

is not an isosceles trapezoid.

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Q10

**a)** Verify that quadrilateral `PQRS`

is a rhombus.

**b)** Verify that the diagonals of `PQRS`

bisect each other.

**c)** Verify that the diagonals of `PQRS`

meet at right angles.

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Q12

A new hospital will serve the four small towns shown on the map. Where would you build the hospital? Justify this location.

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Q13

The vertices of `\triangle EFG`

are `E(-3, 5), F(0, -1),`

and `G(6, 5)`

.

**a)** Find the coordinates of the point of intersection of the medians of `\triangle EFG`

.

**b)** Find the coordinates of the point of intersection of the right bisectors of the sides of `\triangle EFG`

.

**c)** Find the coordinates of the point of intersection of the altitudes of `\triangle EFG`

.

**d)** Verify that these three points of intersection are collinear.

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Q14