A right angle is a 90-degree angle, formed by two perpendicular lines. In geometric terms, a right angle is formed when two lines intersect in such a way that they form four equal angles, each measuring 90 degrees.

- Measures 90 degrees
- Forms a perfect L-shape
- Divides a straight line into two equal parts
- Commonly denoted by a small square at the vertex of the angle

**Example 1:** The corner of a book forms a right angle.

**Example 2:** The letter "L" has two right angles at the corners.

- Right angles are always congruent (i.e., they have the same measure).
- When two right angles are adjacent (i.e., share a common vertex and one common side), they form a straight angle, which measures 180 degrees.

To understand and work with right angles effectively, it's important to remember the following key points:

- Identify right angles in various geometric shapes and everyday objects.
- Understand the concept of perpendicular lines and how they create right angles when they intersect.
- Practice measuring and drawing right angles using a protractor and ruler.
- Explore the relationship between right angles and other types of angles, such as acute angles and obtuse angles.

By mastering the concept of right angles, you'll be able to tackle more advanced geometric problems and gain a deeper understanding of spatial relationships in both two-dimensional and three-dimensional figures.

.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.