Geometry 6-1 Angles of Polygons- Day 1

A polygon is a plane figure formed by a finite number of segments such that (1) sides that have a common endpoint are noncollinear and (2) each side intersects exactly two other sides, but only at their endpoints.

Given the name of the polygons with the following sides 3 sides__________________ 8 sides__________________ 4 sides__________________ 9 sides__________________ 5 sides__________________ 10 sides__________________ 6 sides__________________ 12 sides__________________ 7 sides__________________ 13 sides__________________

Regular Polygon: All angles and all sides are equal What is the name of a regular four sided figure?______________ What is the name of a regular three sided figure?______________

Complete the activity Draw as many triangles as possible from one vertex. Fill in the chart. Then answer the questions related to the activity

Convex polygon

Number of Sides

Number of Triangles

Sum of the Interior angles

Regular Polygon One Interior Angle

Regular Polygon One Exterior Angle

Sum of the Exterior Angles

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

1. What did you learn about the sum of the interior angles of a polygon? Write a formula or equation to find it.

2. What did you learn about the sum of the exterior angles of a polygon?

3. How do you find one exterior angle of a regular polygon? Write a formula or equation to find it.

4. What is the relationship between the interior angle and the exterior angle?

Complete the following after you are done with the activity- Round to the tenths. 1. What is the measure of the interior angle of a regular 15-gon?

2. What is the measure of the exterior angle of a regular 21-gon?

3. What is the sum of the measures of the interior angles of a 17-gon?

4. What is the sum of the measures of the exterior angles of a l4-gon?

5. What is the measure of the interior angle of a regular 18gon?

6. What is the sum of the measures of the interior angles of a 22-gon?

Geometry 6-1 Angles of Polygons- Day 2 Sum of the interior angles of a polygon: One angle in a regular polygon: Sum of the exterior angles of a polygon: One exterior angle of a regular polygon: Interior angle + Exterior angle = 180

Complete the problems 1. Find the sum of the measure of the interior angles of a 30-gon 2. The measure of the interior angle of a regular polygon is 165 degrees. Find the number of sides. 3.

4. Find the measure of one exterior angle of a dodecagon. 5. What is the sum of the exterior angles of a nonagon? 6. A decagon has 5 angles that are 120, 3 angles that are 150, and one that is 170. Find the tenth angle. 7. The exterior angles of a pentagon are 8x, 8x, 7x, 5x, and 5x + 20. What is the value of x?

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A B

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Geometry 6-2 Parallelograms

Definition of Parallelogram: a quadrilateral with

both pairs of opposite sides parallel Which of the following are the characteristics of a parallelogram? Place a check mark by each one that is. You may need to draw in the diagonals 1. Opposite side are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. Adjacent angle are supplementary 5. Diagonals are equal 6. Diagonals bisect the angles 7. Diagonals bisect each other. 8. Diagonals are perpendicular Complete the following. Find the value of the variable(s) 1. 2. 3. 4.

5. In parallelogram RSTV, diagonals intersect at Q. If RQ = 5x+ 1 and QT = 3x + 15, find QT. 6. COORDINATE GEOMETRY Find the coordinates of the intersection of the diagonals of quadrilateral HJKL with the given vertices. (1, 1), J(2, 3), K(6, 3), L(5, 1) You may draw a rough sketch but you may not graph on graph paper

100

70

Geometry 6-3 Tests for parallelograms Are the following parallelograms? 1. 2. 3.

Tests for parallelogram. How do we decide of the shape is a parallelogram? 1. Both sets of opposite sides are equal 2. Both sets of opposite angles are equal 3. One pair of sides equal and parallel 4. Diagonals bisect 5. Both sets of opposite sides are parallel Find x and y so that the quadrilateral is a parallelogram.

Determine if each quadrilateral is a parallelogram. Justify your answer.

Graph each quadrilateral with the given vertices. Determine whether the figure is a parallelogram. Justify your answer with the method indicated.

2.

Geometry 6-4 Rectangles Definition of Rectangle: a parallelogram (opposite sides are parallel) with 4 right angles.

Which of the following are the characteristics of a rectangle? Place a check mark by each one that is. 1. Opposite side are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. Adjacent angle are supplementary 5. Diagonals are equal 6. Diagonals bisect the angles 7. Diagonals bisect each other. 8. Diagonals are perpendicular Complete the following. Each figure is a rectangle. 1. Quadrilateral RUTS is a rectangle. If m<STR = 8x + 3 and m<UTR = 16x - 9, find m<STR. 2. Find the value of x and y

3. If m<DBC = 10x and m<ACB = 4x2- 6, find m< ACB.

4. Find all the angle measures if the m<1= 37

Geometry 6-5 Rhombi and Squares- Rhombus: a parallelogram with 4 congruent sides Which of the following are the characteristics of a rhombus? Place a check mark by each one that is. 1. Opposite side are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. Adjacent angle are supplementary 5. Diagonals are equal 6. Diagonals bisect the angles 7. Diagonals bisect each other. 8. Diagonals are perpendicular Complete the problems related to a rhombus

1. Find the measure of <4 2. Find the measure of <DAC 3. Find the measure of <1

Square: parallelogram with four congruent sides

and 4 right angles. Which of the following are the characteristics of a square? Place a check mark by each one that is. 1. Opposite side are parallel 2. Opposite sides are equal 3. Opposite angles are equal 4. Adjacent angle are supplementary 5. Diagonals are equal 6. Diagonals bisect the angles 7. Diagonals bisect each other. 8. Diagonals are perpendicular

Complete the problems related to a square 1. Find the measure of <ACB

2. Find the measure of <AEC

3. Find the measure of AB if AE=4

MNPQ is a square. If PQ = 3 √2_ and AP = 3, find each measure

E

Must check length of diagonals and slopes of diagonals. You will not be able to graph these on a test or a quiz.

Rhombus: perpendicular diagonals Rectangle: equal diagonals Square: Diagonals are equal and the diagonals are perpendicular. Every square is also a rhombus Every square is also a rectangle

Geometry 6-6 Trapezoid and Kite Definition of Trapezoid: Quadrilateral with exactly one pair of parallel sides.

Median of a trapezoid: Median= b1 + b2

2 Isosceles trapezoid: the legs are congruent

1. Given MN is the median. Find x.

2.

3.

Definition of a kite: quadrilateral with exactly two pairs of consecutive side congruent. Opposite side of a kite are not congruent

1.

You will have to find the slopes of the sides. Determine the parallel sides and then find the distance of the nonparallel sides.