Chapter

Chapter 3
Section

Practice Test Geometric Test

Purchase this Material for $4

You need to sign up or log in to purchase.

Solutions
13 Videos

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

Buy to View

Q1

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

Buy to View

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

Buy to View

Q3

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

Buy to View

Q4

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

is isosceles.

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

lies at `(6, -1)`

.

Buy to View

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.

Buy to View

Q6

Use analytic geometry to verify that quadrilateral `JKLM`

is a rhombus.

Buy to View

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.

Buy to View

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.

Buy to View

Q9

Verify that quadrilateral `ABCD`

is not an isosceles trapezoid.

Buy to View

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.

Buy to View

Q12

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

Buy to View

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.

Buy to View

Q14