Math 3 Honors Geometry
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.
