Chapter Review Geometric Properties
Chapter
Chapter 3
Section
Chapter Review Geometric Properties
Solutions 11 Videos

a. Define a median.

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

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.

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.

2.16mins
Q3ab

Verify that \triangle DEF is a right triangle.

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.

2.12mins
Q5

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

1.19mins
Q7a

Verify that quadrilateral JKLM is a trapezoid.

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.

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.

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.