Chapter

Chapter 3
Section

Chapter Review Geometric Properties

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Solutions
11 Videos

a. Define a median.

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

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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.

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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.

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2.16mins

Q3ab

Verify that `\triangle DEF`

is a right triangle.

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0.55mins

Q4

a. Verify that the altitude from vertex `J`

________ side `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.

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2.12mins

Q5

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

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1.19mins

Q7a

Verify that quadrilateral JKLM is a trapezoid.

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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`

.

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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.

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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.

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0.00mins

Q11

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

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Q12