a. Define a median.
b. List two additional properties of the medians of a triangle.
Use congruent triangles to show how the lengths of the medians to the two equal sides of an isosceles triangle are related.
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.
\triangle DEF is a right triangle.
a. Verify that the altitude from vertex
KL in the triangle with vertices
J(-5, 4), K(1, 8), and
L(-1, -2). Fill in the blank
\triangle JKL. Explain your reasoning.
Show that the line segment joining the midpoints of opposite sides of any parallelogram bisects the area of the parallelogram.
Verify that quadrilateral JKLM is a trapezoid.
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
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.
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.
How would you find the location that is equal distance to three locations on a map? Describe.