Standard 1: Prove and apply geometric theorems to solve problems.

Students are given the measure of one interior angle of an isosceles triangle and are asked to find the measure of another interior angle.

Type: Formative Assessment

Students are given parallelogram ABCD along with midpoint E of diagonal AC and are asked to determine the relationship between the lengths AE + ED and BE + EC.

Type: Formative Assessment

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measure of an angle opposite one of the given angles.

Type: Formative Assessment

Students are asked to prove the Triangle Inequality Theorem.

Type: Formative Assessment

Students are asked to explain why the sum of the lengths of the diagonals of an isosceles trapezoid is less than its perimeter.

Type: Formative Assessment

Students are asked to explain how to determine whether a four-sided frame is a rectangle using only a tape measure.

Type: Formative Assessment

Students are asked to explain why a pair of triangles formed by the sides and diagonals of a parallelogram are congruent.

Type: Formative Assessment

Students are given expressions that represent the measures of two angles of a parallelogram and are asked to find the measures of all four angles describing any theorems used.

Type: Formative Assessment

Students are asked to explain why a quadrilateral formed by drawing the midsegments of a triangle is a parallelogram and to find the perimeter of the triangle formed by the midsegments.

Type: Formative Assessment

Students are asked to explain why the sum of the measures of the interior angles of a convex n-gon is given by the formula (n – 2)180°.

Type: Formative Assessment

Students are given the lengths of two sides of a triangle and asked to describe all possible lengths of the remaining side.

Type: Formative Assessment

Students are asked to describe a triangle whose vertices are the endpoints of a segment and a point on the perpendicular bisector of a segment.

Type: Formative Assessment

Students are given a triangle in which the midpoints of two sides are shown and are asked to describe a method for locating the midpoint of the remaining side using only a straight edge and pencil.

Type: Formative Assessment

Students are asked to find the measures of angles formed by three concurrent lines and to justify their answers.

Type: Formative Assessment

Students are asked to find the measures of angles formed by two parallel lines and two transversals.

Type: Formative Assessment

Students are asked to find the measures of angles formed by two parallel lines and a transversal.

Type: Formative Assessment

Students are asked to prove the Pythagorean Theorem using similar triangles.

Type: Formative Assessment

Students are asked to find the measure of an angle formed by the support poles of a tent using the properties of geometric shapes.

Type: Formative Assessment

Students are asked to prove that the length of the altitude to the hypotenuse of a right triangle is the geometric mean of the lengths of the two segments of the hypotenuse.

Type: Formative Assessment

Students are asked to prove that if a line intersecting two sides of a triangle divides those two sides proportionally, then that line is parallel to the third side.

Type: Formative Assessment

Students are asked to justify statements of a proof of the AA Similarity Theorem.

Type: Formative Assessment

Students are asked to describe the AA Similarity Theorem.

Type: Formative Assessment

Students are asked to prove that a line parallel to one side of a triangle divides the other two sides of the triangle proportionally.

Type: Formative Assessment

Students are asked to write an informal justification of the AA Similarity Theorem.

Type: Formative Assessment

Students are asked to describe and justify the relationship between same side interior angles.

Type: Formative Assessment

Students are asked to provide an informal justification of the Triangle Sum Theorem.

Type: Formative Assessment

Students are asked to describe and justify the relationship between corresponding angles and alternate interior angles.

Type: Formative Assessment

Students are asked to prove that the diagonals of a rectangle are congruent.

Type: Formative Assessment

Students are asked to prove that a rectangle is a parallelogram.

Type: Formative Assessment

Students are asked to prove that opposite angles of a parallelogram are congruent.

Type: Formative Assessment

Students are asked to prove that the diagonals of a parallelogram bisect each other.

Type: Formative Assessment

Students are asked to prove that opposite sides of a parallelogram are congruent.

Type: Formative Assessment

Students are asked to draw a triangle given the lengths of two of its sides and the measure of a nonincluded angle and to decide if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two sides and their included angle and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two angles and their included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle given the measures of two angles and a non-included side and to explain if these conditions determine a unique triangle.

Type: Formative Assessment

Students are asked to draw a triangle with given angle measures, and explain if these conditions determine a unique triangle.

Type: Formative Assessment

In a diagram involving two parallel lines and a transversal, students are asked to use rigid motion to prove that alternate interior angles are congruent.

Type: Formative Assessment

Students are asked to explain congruence in terms of rigid motions.

Type: Formative Assessment

Students are given a diagram of a county fair and are asked to use similar triangles to determine distances from one location of the fair to another.

Type: Formative Assessment

Students are asked to decide if a basketball goal is regulation height and are given enough information to determine this using similar triangles.

Type: Formative Assessment

Students are asked to prove a specific diagonal of a rhombus bisects a pair of angles.

Type: Formative Assessment

Students are asked to locate a pair of similar triangles in a diagram, explain why they are similar, and use the similarity to find an unknown length in the diagram.

Type: Formative Assessment

Students are asked locate a pair of similar triangles in a diagram, explain why they are similar, and use the similarity to find two unknown lengths in the diagram.

Type: Formative Assessment

Students are asked to construct a line parallel to a given line through a given point.

Type: Formative Assessment

Students are asked to prove that the medians of a triangle are concurrent.

Type: Formative Assessment

Students are asked prove that the measures of the interior angles of a triangle sum to 180°.

Type: Formative Assessment

Students are asked to prove that a point on the perpendicular bisector of a line segment is equidistant from the endpoints of the segment.

Type: Formative Assessment

Students are asked to identify a pair of vertical angles in a diagram and then prove that they are congruent.

Type: Formative Assessment

Students are asked to prove that the base angles of an isosceles triangle are congruent.

Type: Formative Assessment

The lesson begins with a hands-on activity and then an experiment with a GeoGebra-based computer model to discover the Triangle Angle Sum Theorem. The students write and solve equations to find missing angle measures in a variety of examples.

Type: Lesson Plan

Students will develop their knowledge of perpendicular bisectors & point of concurrency of a triangle, as well as construct perpendicular bisectors through real world problem solving with a map.

Type: Lesson Plan

Students will develop their knowledge of mid-segments of a triangle, construct and provide lengths of mid-segments.

Type: Lesson Plan

Students will use their knowledge of graphing concurrent segments in triangles to locate and identify which points of concurrency are associated by location with cities and counties within the Texas Triangle Mega-region.

Type: Lesson Plan

Students will start the lesson by playing a game to review angle pairs formed by two lines cut by a transversal. Once students are comfortable with the angle pairs the teacher will review the relationships that are created once the pair of lines become parallel. The teacher will give an example of a proof using the angle pairs formed by two parallel lines cut by a transversal. The students are then challenged to prove their own theorem in groups of four. The class will then participate in a Stay and Stray to view the other group's proofs. The lesson is wrapped up through white board questions answered within groups and then as a whole class.

Type: Lesson Plan

This is a patty paper-folding activity where students measure and discover the properties of the point of concurrency of the perpendicular bisectors of the sides of a triangle.

Type: Lesson Plan

Explore the construction processes for constructing an angle bisector, copying an angle and constructing a line parallel to a given line through a point not on the line using a variety of tools in this interactive, retro video game-themed tutorial.

NOTE: This tutorial uses both the angle bisector construction and the construction to copy an angle as an extension opportunity to also construct a line parallel to a given line through a point not on the line. Students also learn to identify corresponding angles created when a transversal crosses parallel lines, and discover using Geogebra that these angles are congruent.

Type: Original Student Tutorial

Use properties, postulates, and theorems to prove a theorem about a triangle. In this interactive tutorial, you'll also learn how to prove that a line parallel to one side of a triangle divides the other two proportionally. 

Type: Original Student Tutorial

Reflect for a moment on how to measure tall objects with mirrors and mathematics.

Type: Perspectives Video: Teaching Idea