Khan Academy
Khan Academy: Geometry: Proof Vertical Angles Are Equal
Proof that the measures of vertical angles are equal based on properties of supplementary angles. [4:51]
Khan Academy
Khan Academy: Worked Examples: Geometry: Ca Geometry: Proof by Contradiction
Students explore how to do a geometric proof by contradiction.
Khan Academy
Khan Academy: Geometry: Proof: Opposite Angles of Parallelogram Congruent
This video tutorial demonstrates how to prove that the opposite angles of a parallelogram are congruent based on knowledge of the special angles created when parallel lines are cut by a transversal. [4:08]
Khan Academy
Khan Academy: Geometry: Proof: Diagonals of Parallelogram Bisect Each Other
Demonstrates how to prove that the diagonals of a parallelogram bisect each other based on knowledge of the special angles created when parallel lines are cut by a transversal and the triangle congruency postulates. [9:06]
Khan Academy
Khan Academy: Geometry: Proof: Opposite Sides of Parallelogram Congruent
Demonstrates how to prove that the opposite sides of a parallelogram are congruent based on knowledge of the special angles created when parallel lines are cut by a transversal and the triangle congruency postulates. [8:30]
Khan Academy
Khan Academy: Geometry: Proof Rhombus Area Half Product of Diagonal Length
Demostrates how to prove that one way to find the area of a rhombus is by taking half the product of the diagonals. [5:07]
Khan Academy
Khan Academy: Geometry: Proof Rhombus Diagonals Are Perpendicular Bisectors
Demonstrates how to prove that the diagonals of a rhombus are perpendicular bisectors of each other based on knowledge of properties of parallelogram diagonals, triangle congruency, and supplementary angles. [4:04]
Khan Academy
Khan Academy: Geometry: Ca Geometry: More Proofs
Demonstrates solutions to problems #7-10 of California Geometry released state test questions. Problems address understanding of congruent angle pairs when parallel lines are cut by a transversal, counterexamples, and properties of the...
Khan Academy
Khan Academy: Geometry: Equilateral Triangle Sides and Angles Congruent
In this video tutorial [6:29], the instructor models a proof so show that if the sides of an equilateral triangle are congruent, then all the angles are congruent and vice versa. The instructor uses the knowledge of congruent legs and...
Khan Academy
Khan Academy: Geometry: Two Column Proof Showing Segments Are Perpendicular
In this video tutorial [11:06], the instructor shows how to construct a two-column proof using triangle congruence postulates to prove that two line segments are perpendicular.
Khan Academy
Khan Academy: Geometry: 30 60 90 Triangle Side Ratios Proof
In this video tutorial [6:59], the instructor provides a proof for the relationship among the legs and hypotenuse of 30-60-90 triangles by breaking an equilateral triangle into two congruent triangles and using the Pythagorean threorem.
Khan Academy
Khan Academy: Geometry: Triangle Medians and Centroids (2 D Proof)
This video tutorial [15:15] provides a two-dimensional proof that the centroid is located two-thirds the way along every median of a triangle. This is a follow up to the proof in three-dimensions provided in the video, "Triangle Median...
Khan Academy
Khan Academy: Geometry: Congruent Triangle Proof Example
Demonstrates how to use triangle congruency to prove that a given point is the midpoint of a given line segment. The proof is written in the form of a two-column proof. Practice problems available. [5:46]
Khan Academy
Khan Academy: Geometry: Congruent Parts of Iscosceles Triangles
Proof that if the legs of an isosceles triangle are congruent then the base angles are congruent and vice versa using triangle congruency postulates. The proof is written as a two-column proof. [9:03]
Khan Academy
Khan Academy: Geometry: Circumcenter of a Triangle
Explains using multiple proofs that a point on a perpendicular bisector is equidistant from the endpoints of the segment it bisects. Proofs use triangle congruency postulates. Lays the foundation for understanding the circumcenter of a...
Khan Academy
Khan Academy: Geometry: Right Triangles Inscribed in Circles (Proof)
This video tutorial [5:35] explains that if the diameter of a circle is one of the sides of a triangle inscribed in the circle then the triangle is a right triangle. This video also appears in the strand Geometry: Circles.
Khan Academy
Khan Academy: Geometry: Ca Geometry: Pythagorean Theorem, Compass Constructions
This video tutorial demonstrates solutions to problems #51-55 of the California Geometry released state test questions. Problems address proving and using the Pythagorean theorem and compass constructions. [12:35]
Khan Academy
Khan Academy: Geometry: Corresponding Angle Equivalence Implies Parallel Lines
Proof by contradiction that if two lines cut by a transversal create congruent corresponding angles then the lines are parallel. [5:18]
Khan Academy
Khan Academy: Geometry: Angle Bisector Theorem Proof
Explanation and proof of angle bisector theorem. [8:35]
Khan Academy
Khan Academy: Geometry: Point Line Distance and Angle Bisectors
Proof that a point on the angle bisector is equidistant from each side of the angle and proof that a point that is equidistant from each side of the angle lies on the angle bisector. [10:57]
Khan Academy
Khan Academy: Geometry: Triangle Area Proofs
Proof that the area of any triangle is half the product of the base and the height. Three different types of triangles are used to prove the formula. [10:23]
Khan Academy
Khan Academy: Geometry: Congruent Triangle Example 2
Demonstrates how to use triangle congruency to prove that corresponding sides of congruent triangles are congruent and then identifies other congruent parts in the overlapping triangle diagram. The proof is written in the form of a...
Khan Academy
Khan Academy: Geometry: Triangle Medians and Centroids
This video tutorial [8:59] reviews the definitions of median and centroid in relation to a triangle and proves that the centroid is two-thirds the way along a median. The proof is done be drawing a triangle in three-dimensions.
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