In Exercises 6972, determine the measure of the angle. In

A closed figure in a plane determined by three or more straight line segments is called a(n) .

A polygon whose sides are all the same length and whose interior angles all have the same measure is called a(n) polygon.

Two polygons are similar if their corresponding angles have the same measure and the lengths of their corresponding sides are in .

The sum of the measures of the interior angles of a triangle is .

If the corresponding sides of two similar figures are the same length, the figures are called __________ figures.

The sum of the measures of the interior angles of a quadrilateral is _______.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 714, (a) name the polygon. If the polygon is a quadrilateral, give its specific name. (b) State whether or not the polygon is a regular polygon.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 1522, identify the triangle as (a) scalene, isosceles, or equilateral and as (b) acute, obtuse, or right. The parallel markings (the two small parallel lines) on two or more sides indicate that the marked sides are of equal length.

In Exercises 2328, identify the quadrilateral.

In Exercises 2328, identify the quadrilateral.

In Exercises 2328, identify the quadrilateral.

In Exercises 2328, identify the quadrilateral.

In Exercises 2328, identify the quadrilateral.

In Exercises 2328, identify the quadrilateral.

In Exercises 2932, find the measure of x.

In Exercises 2932, find the measure of x.

In Exercises 2932, find the measure of x.

In Exercises 2932, find the measure of x.

In Exercises 3334, lines l1 and l2 are parallel. Determine the measures of 1 through 12.

In Exercises 3334, lines l1 and l2 are parallel. Determine the measures of 1 through 12.

In Exercises 3540, determine the sum of the measures of the interior angles of the indicated polygon.Pentagon

In Exercises 35-40, determine the sum of the measures of the interior angles of the indicated polygon. Heptagon

In Exercises 3540, determine the sum of the measures of the interior angles of the indicated polygon.Nonagon

In Exercises 3540, determine the sum of the measures of the interior angles of the indicated polygon.Decagon

In Exercises 35–40, determine the sum of the measures of the interior angles of the indicated polygon. Icosagon

In Exercises 35–40, determine the sum of the measures of the interior angles of the indicated polygon. Dodecagon

In Exercises 4146, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1.Triangle

In Exercises 4146, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1.Quadrilateral

In Exercises 4146, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1.Octagon

In Exercises 41–46, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1. Nonagon

In Exercises 4146, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1.Decagon

In Exercises 4146, (a) determine the measure of an interior angle of the named regular polygon. (b) If a side of the polygon is extended, determine the supplementary angle of an interior angle. See Example 1.Icosagon

In Exercises 4752, the figures are similar. Find the length of side x and side y.

In Exercises 47-52, the figures are similar. Find the length of side x and side y.

In Exercises 4752, the figures are similar. Find the length of side x and side y.

In Exercises 47-52, the figures are similar. Find the length of side x and side y.

In Exercises 4752, the figures are similar. Find the length of side x and side y.

In Exercises 4752, the figures are similar. Find the length of side x and side y.

In Exercises 5356, triangles ABC and DEC are similar figures. Determine the length of 3 5 1 1 A B C E Dside BC.

In Exercises 5356, triangles ABC and DEC are similar figures. Determine the length of 3 5 1 1 A B C E Dside DC.

In Exercises 5356, triangles ABC and DEC are similar figures. Determine the length of 3 5 1 1 A B C E Dside AD.

In Exercises 5356, triangles ABC and DEC are similar figures. Determine the length of 3 5 1 1 A B C E Dside BE.

In Exercises 57–62, find the length of the sides and the measures of the angles for the congruent triangles ABC and A’B’C’. The length of side

In Exercises 5762, find the length of the sides and the measures of the angles for the congruent triangles ABC and A B C . 7 14 15 A B C 84 C' B' A' 28 .The length of side AB

In Exercises 5762, find the length of the sides and the measures of the angles for the congruent triangles ABC and A B C . 7 14 15 A B C 84 C' B' A' 28 .The length of side BC

In Exercises 5762, find the length of the sides and the measures of the angles for the congruent triangles ABC and A B C . 7 14 15 A B C 84 C' B' A' 28 .BAC

In Exercises 5762, find the length of the sides and the measures of the angles for the congruent triangles ABC and A B C . 7 14 15 A B C 84 C' B' A' 28 .ACB

In Exercises 57-62, find the length of the sides and the measures of the angles for the congruent triangles ABC and A’ B’ C’. Angle ABC

In Exercises 6368, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A B C D . A 10 B D 11 130 70 C C' 50 D' B' A'.The length of side AD

In Exercises 6368, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A B C D . A 10 B D 11 130 70 C C' 50 D' B' A'.The length of side BC

In Exercises 63–68, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A’B’C’D’. The length of side \(\overline{A^{\prime} B^{\prime}}\)

In Exercises 6368, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A B C D . A 10 B D 11 130 70 C C' 50 D' B' A'.BCD

In Exercises 6368, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A B C D . A 10 B D 11 130 70 C C' 50 D' B' A'.ADC

In Exercises 6368, determine the length of the sides and the measures of the angles for the congruent quadrilaterals ABCD and A B C D . A 10 B D 11 130 70 C C' 50 D' B' A'.DAB

In Exercises 6972, determine the measure of the angle. In the figure, ABC makes an angle of 125 with the floor and l1 and l2 are parallel. F D A B G E C l 2 l 1.GBC

In Exercises 6972, determine the measure of the angle. In the figure, angle ABC makes an angle of \(125^{\circ}\) with the floor and l1 and l2 are parallel. angle EDF

In Exercises 6972, determine the measure of the angle. In the figure, ABC makes an angle of 125 with the floor and l1 and l2 are parallel. F D A B G E C l 2 l 1.DFE

In Exercises 6972, determine the measure of the angle. In the figure, ABC makes an angle of 125 with the floor and l1 and l2 are parallel. F D A B G E C l 2 l 1.DEC

Height of a Silo Steve Runde is buying a farm and needs to determine the height of a silo on the farm. Steve, who is 6 ft tall, notices that when his shadow is 9 ft long, the shadow of the silo is 105 ft long (see diagram above and to the right). How tall is the silo? Note that the diagram is not to scale.

Angles on a Picnic Table The legs of a picnic table form an isosceles triangle as indicated in the figure. If ABC = 80, determine mx and my so that the top of the table will be parallel to the ground. y x 80 C B A

Distances in Minnesota A triangle can be formed by drawing line segments on a map of Minnesota connecting the cities of Austin, Rochester, and St. Paul (see figure below). If the actual distance from Austin to Rochester is approximately 44 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate a) the actual distance from St. Paul to Austin. b) the actual distance from St. Paul to Rochester. 1.5 in. 2.25 in. 0.875 in. St. Paul Austin Rochester

Distances in Illinois A triangle can be formed by drawing line segments on a map of Illinois connecting the cities of Rockford, Chicago, and Bloomington (see figure below). If the actual distance from Chicago to Rockford is approximately 90 miles, use the lengths of the line segments indicated in the figure along with similar triangles to approximate a) the actual distance from Chicago to Bloomington. b) the actual distance from Bloomington to Rockford. Area of detail 3 in. 2 in. 3.1 in. Bloomington Rockford Chicago

List six different types of triangles and in your own words describe the characteristics of each.

List five different types of quadrilaterals and in your own words describe the characteristics of each.

In the figure, DEF is similar to DEF. The length of the sides of DEF is shown in the figure. If the scaling factor of DEF with respect to DEF is 3, determine the length of the sides of triangle DEF. F E D F E D 15 12

In the figure, quadrilateral EFGH is similar to quadrilateral EFGH. The length of the sides of quadrilateral EFGH is shown in the figure. If the scaling factor of quadrilateral EFGH with respect to quadrilateral EFGH is 1 3, determine the length of the sides of quadrilateral EFGH. E H G F 9 9 12 21 E H G F

Height of a Wall You are asked to measure the height of an inside wall of a warehouse. No ladder tall enough to measure the height is available. You borrow a mirror from a salesclerk and place it on the floor. You then move away from the mirror until you can see the reflection of the top of the wall in it, as shown in the figure. a) Explain why triangle HFM is similar to triangle TBM. (Hint: In the reflection of light the angle of incidence, HMF, equals the angle of reflection, TMB. Thus, HMF = TMB.) b) If your eyes are 5 1 2 ft above the floor and you are 2 1 2 ft from the mirror and the mirror is 20 ft from the wall, how high is the wall?

Distance Across a Lake a) In the figure, mCED = mABC. Explain why triangles ABC and DEC must be similar. b) Determine the distance across the lake, DE. A B C D E 356.0 ft 543.0 ft 1404.0 ft Lake Joy

Using the Internet and history of mathematics texts, write a paper on the history and use of the theodolite, a surveying instrument.

Using the Internet and other sources, write a paper on the use of geometry in the photographic process. Include discussions on the use of similar figures.