Congruence

IMPORTANT

Mathematics Solutions from Chapter -1 - Congruence

This chapter consists of topics like Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc etc.

Practice Other Topics from Congruence

Mathematics>Geometry - I>Congruence>Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc

This topic covers various concepts like Transversal of Parallel Lines, , etc.

Mathematics>Geometry - I>Congruence>Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations that preserve distance and angle to those that do not (e.g., translation versus horizontal stretch)

This topic covers various concepts like Distance between Two Parallel Lines, Distance of a Point from Coordinate Axes, etc.

Mathematics>Geometry - I>Congruence>Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself

This topic covers various concepts like Elements of a Parallelogram, Types of Quadrilaterals, etc.

Mathematics>Geometry - I>Congruence>Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments

This topic covers various concepts like Characteristics of a Mirror Image, Rotational Symmetry in a Plane Figure, etc.

Mathematics>Geometry - I>Congruence>Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another

This topic covers various concepts like Rotation of Objects by Half Turn, Pattern, etc.

Mathematics>Geometry - I>Congruence>Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; given two figures, use the definition of congruence in terms of rigid motions to decide if they are congruent

This topic covers various concepts like Sequencing Translations, Sequences of Rigid Motions, etc.

Mathematics>Geometry - I>Congruence>Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent

This topic covers various concepts like Congruence of Geometrical Figures, Corresponding Vertices in Congruent Triangles, etc.

Mathematics>Geometry - I>Congruence>Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions

This topic covers various concepts like Notation for Congruence of Two Triangles, Congruent Figures, etc.

Mathematics>Geometry - I>Congruence>Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment’s endpoints

This topic covers various concepts like Theorem: Lines Which are Parallel to the Same Line are Parallel to Each Other, Theorems, etc.

Mathematics>Geometry - I>Congruence>Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point

This topic covers various concepts like Mid Point Theorem in a Triangle, Triangles on the Same Base and Same Parallels, etc.

Mathematics>Geometry - I>Congruence>Prove theorems about parallelograms. Theorems include: opposite sides are congruent, opposite angles are congruent, the diagonals of a parallelogram bisect each other, and conversely, rectangles are parallelograms with congruent diagonals

This topic covers various concepts like Properties for Diagonals of a Parallelogram, Parallelograms on the Same Base and between the Same Parallels, etc.

Mathematics>Geometry - I>Congruence>Make formal geometric constructions with a variety of tools and methods (compass and straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.). Copying a segment; copying an angle; bisecting a segment; bisecting an angle; constructing perpendicular lines, including the perpendicular bisector of a line segment; and constructing a line parallel to a given line through a point not on the line

This topic covers various concepts like Division of a Line Segment in the Given Ratio Using One Ray, Construction of Line Parallel to a Given Line Using Ruler and Compass, etc.

Mathematics>Geometry - I>Congruence>Construct an equilateral triangle, a square, and a regular hexagon inscribed in a circle

This topic covers various concepts like Construction of a Triangle using Ruler and Compass, Construction of a Quadrilateral Similar to a Given Quadrilateral, etc.