Properties of Parallelograms
True or False, All Parallelogram have Opposite sides are parallel and congruent, Opposite angles are congruent, Consecutive angles supplementary, diagonals bisect each other
What is True
True or False, In Parallelogram ABCD,
Angle A, B,C,D are all right angle, and they have congruent diagonals
Danielle says that means it is a Square
False, it's properties of a Rectangle
True or False, A Mid-segment of a triangle is a segment joining the midpoints of two sides of a triangle and it is parallel to the third side of the triangle.
True
True or False, Similar Triangles are similar if corresponding sides are in proportion and corresponding angles are congruent
True
I have all the properties of a Parallelogram and have 4 congruent sides, diagonals bisect angles, diagonals perpendicular, What am I
What is a Rhombus
Parallelogram ABCD is a Rhombus what is their properties?
All the Parallelogram properties as well as four congruent sides, diagonals bisect angles and diagonals perpendicular
What is the relationship of The Mid-segment theorem
The mid-segment is half the length of the third side of the triangle.
The Ratio of the Perimeters of the similar figure is always_____ to the ratio of the their corresponding sides.
Equal
Parallelogram QSRD Also has 4 congruent sides,diagonals bisect angles,diagonals perpendicular
What am I
What is a Rhombus
Parallelogram ABCD
Given: AC is parallel to BD, AB is congruent to CD, Angle A is congruent to Angle D
Prove: ABCD is a Rhombus
Statements- 1) Angle A is congruent to Angle D, 2) AC is parallel to BD, 3) AC is congruent to BD, 4) Angle C is congruent to Angle B, 5) AB is congruent to CD, 6) ABCD is a Rhombus
Reasons: 1) Given, 2) Given, 3) In a parallelogram, parallel lines are also congruent especially if diagonals angles are congruent to each other, 4) Parallel Lines makes Alt. Int. Angles, 5) Given 6) A Rhombus has four congruent sides.
Triangle ABC is a Dilation of Triangle DEF
AB is 2 and DE is 3, BC is 4
What is EF
X=6
What is the Theorem: If two angles of one triangle are congruent to the two angles of another triangle, the triangles are similar.
AA Similarity
What are the Properties of a Rectangle
Rectangles have all the properties of the parallelogram as well as 4 right angles and congruent diagonals
ABCD is a Rectangle
Givens: AC is congruent to BD, EF is congruent to BD,Angle E,B,D and F are right angles EF bisects AB
Prove: EBFD is a Square
Statements: 1) AC is congruent to BD and EF is congruent to BD, 2) EF bisects AB 3) AE is congruent EB and CF is congruent FD, 4) AB-AE=CD-CF, 5) EB is congruent to FD, 6) Angle E,B,D,and F are right angles, 7) Angle E,B,D,and F are congruent, 8) EBFD is a Square
Reasons: 1)Given,2)Given,3)A bisector divides a segment into two congruent parts, 4) Segment Subtraction,5) Segment Subtraction, 6)Given,7) All right angles are congruent to each other, 8) four congruent sides and 4 right angles.
Triangle ABC is a Dilation of Triangle DEF
AB is 3, BC is 6, CA is 9
DE is 4
What is the Perimeter of DEF
Perimeter of DEF is 24
What is the Altitude Rule- SAAS
The Altitude to the hypotenuse of a right triangle is the mean proportional between the segments into which it divides the hypotenuse.