This task provides a construction of the angle bisector of an angle by reducing it to the bisection of an angle to finding the midpoint of a line segment. It is worth observing the symmetry -- for both finding midpoints and bisecting angles, the goal is to cut an object into two equal parts. The conclusion of this task is that they are, in a sense, of exactly equivalent difficulty -- bisecting a segment allows us to bisect and angle (part a) and, conversely, bisecting an angle allows us to bisect a segment (part b). In addition to seeing how these two constructions are related, the task also provides an opportunity for students to use two different triangle congruence criteria: SSS and SAS.

The purpose of this task is primarily assessment-oriented, asking students to demonstrate knowledge of how to determine the congruency of triangles.

This task provides the most famous construction to bisect a given angle. It applies when the angle is not 180 degrees.

This task shows that the three perpendicular bisectors of the sides of a triangle all meet in a point, using the characterization of the perpendicular bisector of a line segment as the set of points equidistant from the two ends of the segment. The point so constructed is called the circumcenter of the triangle.

Students identify, perform, and algebraically describe rigid motions to establish congruence of two dimensional polygons, including triangles, and develop congruence criteria for triangles.

This task is designed to give students insight into the effects of translations, rotations, and reflections on geometric figures in the context of showing that two figures are congruent.

Students' first experience with transformations is likely to be with specific shapes like triangles, quadrilaterals, circles, and figures with symmetry. Exhibiting a sequence of transformations that shows that two generic line segments of the same length are congruent is a good way for students to begin thinking about transformations in greater generality.

This task has two goals: first to develop student understanding of rigid motions in the context of demonstrating congruence. Secondly, student knowledge of reflections is refined by considering the notion of orientation in part (b).

The construction of the perpendicular bisector of a line segment is one of the most common in plane geometry and it is undertaken here. In addition to giving students a chance to work with straightedge and compass, the problem uses triangle congruence both to show that the constructed line is perpendicular to AB and to show that it bisects AB.

This lesson [2:00] will define the phrase corresponding parts (e.g. angles, sides, etc.). It is 1 of 5 in the series titled "Corresponding Parts."

This lesson [4:27] will define the phrase corresponding parts (e.g. angles, sides, etc.). It is 2 of 5 in the series titled "Corresponding Parts."

Use the triangle congruence criteria SSS, SAS, ASA, and AAS to determine that two triangles are congruent. Students receive immediate feedback and have the opportunity to try questions repeatedly, watch a video or receive hints.

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Students, teachers, and parents alike will enjoy this challenging math site. It contains a clever brain teaser section plus creative problems related to algebra, geometry, measurement, numbers, statistics, and probability. A Spanish version is available.

This tasks examines how to calculate the area of an equilateral triangle using high school geometry.

This task "Uses facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure (7.G.5)" except that it requires students to know, in addition, something about parallel lines, which students will not see until 8th grade.

This concept introduces students to the ASA and AAS Triangle Congruence shortcuts. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.

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In this lesson students compare sides and angles in triangles. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.

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This concept teaches students how to write congruence statements and use congruence statements to determine the corresponding parts of triangles. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.

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In this lesson students deduce information about triangles with congruence statements. Students examine guided notes, review guided practice, watch instructional videos and attempt practice problems.

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