Conditional Statments
If ABCD is a square, then it has four right angles.
Is the converse of this statement true? Why or why not?
No. A rectangle has four right angles but it is not a square.
I can't afford to buy the features on this thing so lettuce switch to good notes :D
Triangle ABD cong Triangle CBE: SAS
Triangle ABE cong Triangle CBD: SAS; ASA, SSS
A quadrilateral is a rhombus if and only if
its diagonals bisect the opposite angles
Fill in the blank:
If two parallel lines are cut by a transversal, the _____________ are congruent.
alternate interior angles
A parallelogram is a rhombus if and only if its diagonals bisect the opposite angles.
If a parallelogram is a rhombus, its diagonals bisect the opposite angles.
If the diagonals of a parallelogram bisect the opposite angles, then the parallelogram is a rhombus.
Illustrate the appropriate construction to draw the altitude of a triangle.
I will draw on board
Which of the following are true:
(a) All squares are rhombi.
(b) All rectangles are parallelograms.
(c) All parallelograms with congruent diagonals are rectangles.
(d) All rhombi with congruent diagonals are squares
All of them
Angle 1 = 39 degrees
Angle 2 = 103 degrees
Angle 3 = 38 degrees
Fill in the blank:
Given a quadrilateral, it is a _____________ if both pairs of opposite sides are congruent.
Parallelogram
Another picture... why do we have to pay for this thing...
Angle 1 = 145 degrees
What attributes do a square and a rectangle share? (attributes specific to these quadrilaterals)
- four right angles
- congruent diagonals
Provide an informal proof for the following statement:
If two lines are both perpendicular to a transversal, then the lines are parallel.
(1) Transveral t is perp. to line m; Transveral t is perp. to line n
(2) Angles 1, 2, 3, 4, 5, 6, 7, and 8 = 90 degrees (defn of perp)
(3) Alternate interior angles are congruent so line m and n are parallel
True or false:
A trapezoid can be a parallelogram.
No. Our textbook defines a trapezoid as having _____ set of parallel lines.
Still poe...
Make an informal outline of the following proof:
- AB cong BC (midpoint defn)
- Angle ABD = Angle CBD = 90 degrees (given)
- BD = BD (identity)
- Triangle ABD cong Triangl CBD (SAS)
The area of a square is 25 in2. Find the length of the diagonals.
sqrt(50) or 5 sqrt(2)
Provide a formal proof for the following corollary:
If two lines are parallel and a line is perpendicular to one of the two lines, then it is perpendicular to the other line.
(1) Line m and n are parallel; line t is perpendicular to line m ---- (1) given
(2) angles 1, 2, 3, and 4 = 90 degrees ----- (2) defn of perp
(3) angle 3 cong angle 6 =90 degrees ----- (3) Thm 5.5 alt interior angles are congruent
(4) Line t is perp to line n ---- (4) Defn of perp