An angle is the figure formed by two rays, called the sides of the angle, sharing a common endpoint, called the vertex of the angle.

**1. Acute Angle:** An angle that measures between 0 and 90 degrees.

**2. Right Angle:** An angle that measures exactly 90 degrees.

**3. Obtuse Angle:** An angle that measures between 90 and 180 degrees.

**4. Straight Angle:** An angle that measures exactly 180 degrees.

Angles are typically measured in degrees. A complete revolution is 360 degrees, and a straight angle is half of a revolution, so it measures 180 degrees.

**1. Complementary Angles:** Two angles are complementary if the sum of their measures is 90 degrees.

**2. Supplementary Angles:** Two angles are supplementary if the sum of their measures is 180 degrees.

**3. Vertical Angles:** When two lines intersect, the angles opposite each other are called vertical angles and are equal in measure.

Angles are typically denoted using three points, with the vertex in the middle. For example, angle ABC can be denoted as ∠ABC.

An angle bisector is a ray which divides an angle into two equal angles.

- Find the measure of the complement of a 35-degree angle.
- If two angles are supplementary and one measures 120 degrees, what is the measure of the other angle?

Understanding angles and their properties is crucial in geometry and trigonometry. Practice identifying and measuring angles to strengthen your knowledge of this fundamental concept.

.Study GuideSimilarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer key

Similarity and scale Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons Worksheet/Answer keyUsing Similar Polygons Worksheet/Answer keySimilar Polygons

Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.