Chapter

Chapter 3
Section

Chapter Review Geometric Properties

Purchase this Material for $8

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
11 Videos

a. Define a median.

b. List two additional properties of the medians of a triangle.

Buy to View

1.07mins

Q1

Use congruent triangles to show how the lengths of the medians to the two equal sides of an isosceles triangle are related.

Buy to View

0.58mins

Q2

a. Draw a right triangle with the shorter sides aligned with the coordinate axes. Then, draw the right bisectors of all three sides.

b. Show that the point of intersection of the right bisectors of the sides of any right triangle lies on the hypotenuse.

Buy to View

2.16mins

Q3ab

Verify that `\triangle DEF`

is a right triangle.

Buy to View

0.55mins

Q4

a. Verify that the altitude from vertex `J`

bisects `KL`

in the triangle with vertices `J(-5, 4), K(1, 8)`

, and `L(-1, -2)`

. Fill in the blank

b. Classify `\triangle JKL`

. Explain your reasoning.

Buy to View

2.12mins

Q5

Show that the line segment joining the midpoints of opposite sides of any parallelogram bisects the area of the parallelogram.

Buy to View

1.19mins

Q7a

Verify that quadrilateral JKLM is a trapezoid.

Buy to View

0.50mins

Q8

a. Classify the quadrilateral with vertices `T(2, 4), U(8, 2), V(7, -1)`

, and `W(1, 1)`

. Justify this classification.

b. Verify a property of the diagonals of `TUVW`

.

Buy to View

2.28mins

Q9

a. Show that `A(-12, -5)`

and `B(12, 5)`

are endpoints of a diameter of the circle defined by `x^2 + y^2 = 169`

.

b. State another point `C`

on the circle and show that `\triangle ABC`

is a right triangle.

Buy to View

4.00mins

Q10abc

a. Verify that points `P(5, 7)`

and `Q(7, -5)`

lie on the circle with equation `x^2 + y^2 = 74`

.

b. Verify that the right bisector of the chord `PQ`

passes through the centre of the circle.

Buy to View

0.00mins

Q11

How would you find the location that is equal distance to three locations on a map? Describe.

Buy to View

Q12