In geometry, to bisect something means to divide it into two equal parts. This can apply to lines, angles, or shapes. When a line or angle is bisected, it is divided into two equal parts.

To bisect a line segment, follow these steps:

- Use a ruler to draw the line segment you want to bisect.
- With a compass, place the pointed end at one end of the line segment and draw an arc that crosses the line.
- Without changing the compass width, place the pointed end at the other end of the line segment and draw another arc that crosses the first arc.
- Draw a straight line connecting the two intersection points of the arcs. This line will bisect the original line segment into two equal parts.

To bisect an angle, follow these steps:

- Use a protractor to draw the angle you want to bisect.
- With a compass, place the pointed end at the vertex of the angle and draw an arc that intersects both sides of the angle.
- Without changing the compass width, place the pointed end at one of the intersection points and draw another arc inside the angle.
- Repeat the previous step using the other intersection point.
- Draw a straight line from the vertex of the angle to the intersection point of the two arcs. This line will bisect the angle into two equal parts.

1. Bisect the line segment AB, where A = (2, 4) and B = (6, 8).

2. Bisect the angle XYZ, where angle XYZ = 120 degrees.

Once you have understood and practiced the above steps, you will have a good grasp of the concept of bisecting in geometry.

.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.