Geometry Crash Course 2022: Learn Geometry in 11 Hours

Explore triangles classified by angle size, identifying acute triangles with all angles under 90 degrees, right triangles with a 90-degree angle, and obtuse triangles with an angle over 90 degrees.

Identify triangle types based on side length: scalene with no equal sides, isosceles with two equal sides, and equilateral with all three sides equal.

Demonstrate why the three interior angles of any triangle sum to 180 degrees, using a parallel line construction and angle equalities to prove the theorem.

Construct a parallel through vertex a to bc and prove via alternate angles that the sum of a triangle's interior angles equals two right angles.

This lecture proves that the exterior angle of a triangle equals the sum of its two opposite interior angles, using extension of a side and angle sums.

Explore the side-side-side (SSS) condition for congruent triangles by matching corresponding sides. See how congruent triangles have equal corresponding parts, including angles.

Explore the sas congruence theorem: if two sides and the included angle of one triangle equal the corresponding parts of another, the triangles are congruent.

Learn the ASA congruence rule for triangles: two angles and the included side determine triangle congruence, with corresponding angles and sides matching and opposite sides aligning.

Apply the right-angle hypotenuse side congruence rule: if a right triangle shares equal hypotenuse and one corresponding side with another, the triangles are congruent.

Discover how two angles and a side establish triangle congruence by matching corresponding angles and sides, proving triangles are congruent through this reasoning.

Show that the base angles of an isosceles triangle are equal by using equal sides and congruent right triangles formed from a perpendicular.

Explore the converse: when two angles in a triangle are equal, the sides opposite them are equal, proving the isosceles property.

Prove that in a triangle with two equal sides, the angle bisector of the vertical angle is perpendicular to the base and bisects it, using congruent triangles and angle reasoning.

Explore the median from the vertex to the base midpoint; show it bisects the base and is perpendicular in isosceles triangles, using congruent triangles and angle properties.

Explore theorem 1 in triangles by drawing the line through a midpoint parallel to a side, revealing congruent triangles, equal segments, and the role of alternate angles in proofs.

Theorem 2 states that the segment joining the midpoints of two sides of a triangle is parallel to the third side and half its length.

Learn that the sum of the angles in a triangle equals two right angles and use this to find unknown angles from a + b + c = 180.

Explore how exterior angles of a triangle equal the sum of the opposite interior angles, and apply parallel lines and alternate angles to solve problems.

Explore the isosceles triangle, proving base angles are equal when two sides are equal, and apply the triangle angle sum and exterior angle theorems to solve problems.

Apply the midpoint theorem to triangles by drawing a line through the midpoint parallel to the opposite side, giving a segment half the third side and revealing median relationships.

Understand quadrilaterals as four-sided figures bounded by four line segments and learn to find their area using a diagonal and lines from opposite vertices.

Explore trapezium properties, including two opposite parallel sides, bases and legs, and the mid-segment, with methods to draw and calculate area from bases and height.

Explore parallelogram properties: opposite sides are parallel and equal, opposite angles are equal, diagonals bisect each other, and perpendicular height helps with construction, while area formulas are not the focus.

Explore rectangle fundamentals by identifying its 90-degree angles, opposite sides being equal, and its diagonals being equal. Learn how these properties define a rectangle.

Explore the geometry of squares, where all sides are equal and angles are 90 degrees. Learn how diagonals intersect, create congruent triangles, and compute area from side or diagonal.

Learn that a rhombus has all sides equal, while its diagonals are not necessarily equal. Compare it to rectangles and squares, noting that rhombus angles need not be 90 degrees.

Prove that opposite sides and opposite angles of a parallelogram are equal by showing congruent triangles and using alternate interior angles.

This lecture proves that a quadrilateral with opposite sides equal is a parallelogram by showing opposite sides are parallel and using alternate interior angles.

The lecture shows that in a parallelogram, opposite angles are equal and opposite sides are parallel, using angle sums and alternate interior angles to prove parallelism.

Lecture proves the converse of theorem 3, showing that ed equals bc and ed parallel bc implies ab equals cd and ab parallel cd, via triangle similarity and alternate angles.

This lecture presents the converse of theorem 3, showing that opposite sides are equal and parallel, and uses triangle congruence via alternate angles and corresponding sides to prove the claim.

Prove that in a parallelogram, diagonals bisect each other by constructing congruent triangles using alternate interior angles and equal opposite sides.

Explain that a quadrilateral whose diagonals bisect each other is a parallelogram, using triangle congruence and parallelism to establish opposite sides are parallel.

Master the parallelogram theorem through practical exercises. Prove opposite sides and opposite angles are equal and apply diagonals to solve lengths and angles.

This lecture proves that parallelograms on the same base and between the same parallel lines have equal areas, using two methods: subtracting triangular areas and corresponding angles.

Show that on the same base and between the same parallels, the area of a triangle equals half the area of the parallelogram built on that base.

Theorem 3 shows that triangles on the same base between parallel lines have equal areas. It states that a triangle’s area equals half the base times the height.