Math 3 Honors Geometry

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Properties of Rhombus

1. ALL parallelogram properties apply 2. All Sides are congruent 3. Diagonals are perpendicular 4. Diagonals bisect angles

Provings any quadrilateral is a parallelogram

1. Both pairs of opposite sides are parallel 2. Both pairs of opposite sides are congruent 3. Both pairs of opposite angles are congruent 4. On interior angle is supplementary to both consecutive angles. 5. Diagonals bisect each other 6. One pair of opposite sides are both congruent and parallel If 3 or more parallel lines cut one transversal into congruent segments,then it cuts all transversals into congruent segments

Properties of a trapezoid

1. Legs are congruent 2. Pairs of base angles are congruent 3. Diagonals are congruent

Number of Properties of Parallelograms

5

perpendicular bisector of a triangle

A line that is perpendicular to a segment at its midpoint.

Rhombus

A parallelogram with four congruent sides

Rectangle

A parallelogram with four right angles

Trapezoid

A quadrilateral with exactly one pair of parallel sides

angle bisector of a triangle

A segment that bisects an angle of the triangle and has one endpoint at a vertex of the triangle and the other endpoint at another point on the triangle.

A quadrilateral is a parallelogram if one pair of opposite sides is congruent and parallel

Always

If a parallelogram has one right angle, then the other angles are right angles

Always

If a quadrilateral has four right angles, then it is a rectangle.

Always

The midsegment's length is always the _____________________ of the two bases

Average

The parallel sides of a trapezoid are called the _________________.

Bases

A parallelogram is a rhombus

False

A rectangle is a square

False

A trapezoid is a parallelogram

False

Consecutive angles of a parallelogram are congruent

False

Consecutive sides of a parallelogram are congruent

False

Diagonals of an isosceles trapezoid bisect each other

False

If a parallelogram has congruent diagonals. Then it is a square

False

If the diagonals of a quadrilateral are perpendicular to each other. Then the quadrilateral is a rhombus

False

The diagonals of a parallelogram are congruent

False

The diagonals of a trapezoid are congruentent

False

The centroid falls outside the triangle only when the triangle us obtuse

False. The centroid is ALWAYS inside the triangle.

Median

Goes from a vertex to the midpoint of the opposite side of a triangle

If the legs of a trapezoid are congruent, it is called an ______________ trapezoid.

Isosceles

The non- parallel sides in a trapezoid are called _________

Legs

The segments of the midpoints of the legs is the

Midsegment(median)

An isosceles trapezoid is a parallelogram

Never

1. Both pairs of opposite sides are parallel. 2. Both pairs of opposite sides are congruent. 3. Both pairs of opposite angles are congruent. 4. Consecutive angles are supplementary. 5. The diagonals bisect each other.

Properties of a Parallelogram

A parallelogram with four right angles and four congruent sides is a square

So a square is always a rectangle and a rhombus

If a parallelogram is equilateral,then it is equilangular.

Sometimes

Centroid

The point of concurrency of the medians of a triangle. It ALWAYS falls inside the triangle. The centroid splits the median in a ratio of 2:1 (The "big part" is 2 times the "small part")hIn other words, the distance from the vertex to centroid is 2/3 the distance of the entire median

A reactangle is equiangular

True

A square is a rectangle

True

A square is a rhombus

True

A square is both a rectangle and rhombus

True

In a quadrilateral, if one pair is opposite sides are congruent and parallel, then it is a parallelogram

True

Lower base angles and upper base angles are congruent in an isosceles trapezoid

True

Opposite angles of an isosceles trapezoid are supplementary

True

Opposite sides of a parallelogram are congruent

True

The centroid is the center of gravity

True

The circumcenter falls on the triangle when the triangle is right.

True

The diagonals of a parallelogram bisect each other

True

The diagonals of a rectangle bisect opposite angles

True

The diagonals of a rhombus are perpendicular bisects of each other

True

The diagonals of a rhombus are perpendicular to each other

True

The diagonals of rectangle are congruent

True

The incenter always falls inside the triangle

True

The midpoint of the hypotenuse of a right triangle is always the circumcenter of that angle

True

Parallelogram

a quadrilateral with both pairs of opposite sides parallel

Properties of a rectangle

all properties of a parallelogram, all angles are right, diagonals are congruent

Incentor

the point of concurrency of the 3 angle bisectors of a triangle (always falls inside a triangle). It is equidistant from the sides of the triangle. It is the center of the inscribed circle.

Circumcenter

the point of concurrency of the perpendicular bisectors of a triangle. It is equidistant from the vertices of the triangle. It is the center of the circumscribed circle.


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