Find the measure of each unknown angle.
Find the measure of each unknown angle.
Find the measure of each unknown angle.
Find the measure of each unknown angle.
Explain why the angle relationships shown are not possible.
For each description , draw an example of the triangle or explain why it cannot exist.
a triangle with an obtuse exterior angle
For each description , draw an example of the triangle or explain why it cannot exist.
a triangle with three acute exterior angles
Calculate the measure of each unknown angle.
Calculate the measure of each unknown angle.
Calculate the measure of each unknown angle.
Calculate the measure of each unknown angle.
For each description, draw an example of the quadrilateral or explain why it cannot exist.
a quadrilateral with three acute interior angles
For each description, draw an example of the quadrilateral or explain why it cannot exist.
a quadrilateral with four acute interior angles
Find the sum of the interior angles of each polygon.
pentagon
Find the sum of the interior angles of each polygon.
heptagon (7-sided figure)
Find the sum of the interior angles of each polygon.
pentadecagon (15-sided figure)
Find the sum of the interior angles of each polygon.
undecagon (11-sided figure)
Find the sum of the interior angles of each polygon.
octagon
Find the measure of the interior angle of a regular polygon with 6 sides.
Find the measure of the interior angle of a regular polygon with 7 sides.
Find the measure of the interior angle of a regular polygon with 12 sides.
Find the measure of the interior angle of a regular polygon with 15 sides.
How many sides does a polygon have if the sum of its interior angles is 1080^{\circ}?
How many sides does a polygon have if the sum of its interior angles is 1260^{\circ}?
a) Construct a regular hexagon.
b) Describe the method you used.
Show that the area of \triangle DGH is one quarter of the area of \triangle DEF.
For each of these statements, either explain why it is true or draw a counter-example to show that it is false.
The median to the vertex opposite the unequal side of an isosceles triangle bisects the angle at the vertex.
For each of these statements, either explain why it is true or draw a counter-example to show that it is false.
The medians of an isosceles triangle are equal in length.
For each of these statements, either use a diagram to help explain why the statement is true, or draw a counter-example and explain why the statement is false.
A line segment joining the midpoints of opposite sides of a rhombus bisects its area.
For each of these statements, either use a diagram to help explain why the statement is true, or draw a counter-example and explain why the statement is false.
A line segment joining the midpoints of two sides of a parallelogram bisects the area of the parallelogram.
For each of these statements, either use a diagram to help explain why the statement is true, or draw a counter-example and explain why the statement is false.
A line segment joining the midpoints of the parallel sides of a trapezoid bisects its area.
For each of these statements, either use a diagram to help explain why the statement is true, or draw a counter-example and explain why the statement is false.
The diagonal of a trapezoid bisects the area.
Describe how you can use geometry software to determine the types of quadrilaterals in which the diagonals bisect the area of the quadrilateral.