Proofs In Two Columns That Involve Quadrilaterals with Triangle Inequality and Congruence.

You understand what the proof is asking you to prove, but how do you layout the solution? What should be the first statement? What should be the last statement and reason? Should you use what properties for quadrilaterals?

You will be given the solution of a set of proofs, each one with a proposed exercise for you to complete to check your understanding. You may take advantge of the opportunity to interact with the lesson. At the upper right corner you will find the pull down menu for MARKER TOOLS that has a pen and a highlighter that may allow you to work the proofs first on your own then check them in the presentation. Don't defeat yourself before starting!

Lesson's Content

Lesson In PDF Format (no animations)

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Lesson's Glossary

Acute triangle
A triangle whose angles are acute.

Angle
Geometry shape formed by two rays (initial and ending sides of the angle) that share a common endpoint called the vertex. You may name an angle using the vertex, or a point in each ray and the vertex label in the center.

Angle-angle-side (AAS) congruence states that if any two consecutive angles of a triangle are equal in measure to two consecutive angles of another triangle and a pair of corresponding not included sides to these angles is congruent; then the two triangles are congruent; that is, they have exactly the same shape and size.

Angle-side-angle (ASA) congruence states that if any two angles of a triangle are equal in measure to two angles of another triangle and the side in between each pair of angles have the same length, then the two triangles are congruent; that is, they have exactly the same shape and size.

Concave polygon
If a polygon has diagonals that lie outside the polygon then the polygon is concave.

Convex polygon
A convex polygon is any polygon that is not concave.

Equilateral triangle
A triangle whose sides are equal in length.

Included angle
The angle made by two sides of a polygon .

Included side
The side between two consecutive angles in a polygon.

Isosceles trapezoid
Trapezoid with two non-congruent and non-parallel sides.

Isosceles triangle
A triangle with two sides of equal length.

Kite
Parallelogram with two pairs of adjacent sides congruent and without opposite sides congruent.

Parallelogram
Any quadrilateral with two pairs of opposite sides parallel.

Polygon
It is a closed plane figure with a least three straight segments as sides.

Quadrilateral
A four-sided polygon.

Rectangle
Any parallelogram that has 4 right angles.

Rhombus
Any parallelogram with 4 congruent sides.

Right triangle
A triangle that has a 90 degree angle.

Scalene triangle
A triangle with no equilateral sides.

Side-angle-side (SAS) congruence states that if any two sides of a triangle are equal in length to two sides of another triangle and the angles between each pair of sides have the same measure, then the two triangles are congruent; that is, they have exactly the same shape and size.

Side-side-side (SSS) congruence states that if the three sides of one triangle have the same lengths as the three sides of another triangle, then the two triangles are congruent.

Square
Parallelogram with four congruent sides and four congruent angles.

Theorem
A theorem in mathematics is a proven fact. A theorem about polygon must be true for every polygon; there can be no exceptions. An idea which works in several different cases is not enough.

Trapezoid
Quadrilateral with exactly one pair of parallel sides.

Vertex of a polygon (plural vertices)
An endpoint of a segment in a polygon.

 

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