1. Parallel and Perpendicular lines
Chapter 3
Parallel and Perpendicular lines

2. Obj: To define and classify special types of quadrilaterals
Chapter 6-1
Obj: To define and classify special types of quadrilaterals

3. QUADRILATERAL MAPPING

4. Helpful Facts
Sum of the interior angles: Triangle– 180 Quadrilateral – 360 Isosceles triangles- two congruent sides and base angles are congruent.

5. Theorems for Parallelogram
Quadrilateral with both pairs of opposite sides are parallel
Opposite sides are congruent.
Opposite angles are congruent.
Consecutive angles are supplementary.
Diagonals bisect each other.

6. Key Concepts Kites Two pairs of adjacent sides are congruent
Diagonals are perpendicular

7. Key Concepts Isosceles Trapezoids One pair of parallel lines
Base angles are congruent
Non-parallel sides are congruent
Diagonals are congruent

8. Key concepts Rhombus Properties
Both Pairs of opposite sides are parallel
Four congruent sides
Both pairs of opposite angles are congruent
Consecutive angles are supplementary.
Diagonals bisect each other
Diagonals are perpendicular
Diagonal bisects each angle
1 2
3 4

9. Key Concepts Rectangles Properties
Both pairs of opposite sides are parallel
Both pairs of opposite sides are congruent
All right angles
Diagonals bisect each
other
Diagonals are congruent

10. Square All sides are congruent
Both pairs of opposite sides are parallel
All right angles (all angles are congruent)
Diagonals bisect each other
Diagonals are congruent
Diagonals are perpendicular bisectors

11. Key Concept
Distance between the two are congruent DF

12. Find the distance between the points to the nearest tenth.
1. M (2, –5), N (–7, 1)
2. X (0, 6), Y (4, 9)
Find the distance between the points to the nearest tenth.
Find the slope of the line through each pair of points.
1. d = √ (x2 – x1)2 + (y2 – y1)2 = √ ( –7 – 2)2 + (1 – (–5))2 =
√( –9) = √ = √ = 10.8
m = 9-6 = 3

13. Graph quadrilateral QBHA.
Determine the most precise name for the quadrilateral with vertices Q(–4, 4), B(–2, 9), H(8, 9), and A(10, 4).
Graph quadrilateral QBHA.
Find the slope of each side.
slope of QB = slope of BH = slope of HA = slope of QA =
9 – 4
–2 – (–4) 5 2 =
9 – 9
8 – (–2)
4 – 9
10 – 8
= –
4 – 4
–4 – 10
Next, use the distance formula to see whether any pairs
of sides are congruent.
QB = ( –2 – ( –4))2 + (9 – 4)2 = =
HA = (10 – 8)2 + (4 – 9)2 = =
BH = (8 – (–2))2 + (9 – 9)2 = = 10
QA = (– 4 – 10)2 + (4 – 4)2 = = 14
QBHA is an isosceles trapezoid.

14. In parallelogram RSTU, m <R = 2x – 10 and m< S = 3x + 50. Find x.
2X-10 +3X+50 = 180
5X +40 = 180
5X = 140
X = 28
R 2X U
3X +5 0
S T

15. Find the measure of the missing angle of the isosceles trapezoid.
Y= 156- base angles are congruent. w = = 24 - adjacent angles are supplementary (same-side interior angles) Z =24 – base angles are congruent

16. Find the missing measures of the kite.
1 = Congruent to 72- isosceles triangle have congruent base angles 2= 90 diagonals are perpendicular 3=180-(90+72) =18 sum of the interior angles of a triangle is 180 degrees.

17. Use KMOQ to find m  O.
= 145
mO = 145

18. Find the value of x in ABCD. Then find m  A.
Oppostite angles are congruent
135-x = x + 15
+ x +x
= 2x + 15
120 = 2x 2
60 = x
D = = 75
A and  D are supplementary
180 – 75 = 105
A = 105

19. Find the values of x and y in KLMN.
Diagonals bisect each other.
2x + 5 = 5y
7y-16 = x
2(7y-16) + 5 = 5y
14y – = 5y
14y – = 5y
= -9y
3 = y
X = 7( 3) – 16 = = 5

20. If AC = 3 and BD = 6, find BF. 6(2) = 12 BF = 12

21. Try: Find y in . Then find mE, mF, mG, m H.
6y + 4 = 3y y = 33 y = 11 mE = mG = 70  mF= m H= 110

22. Try: Find the Values of a and b.
a = b +2 b+10 = 2a -8 Using substitution: b +10 = 2(b+2) -8 b+10 = 2b +4 – 8 10 = b – 4 14 = b a = = 16

23. Try: n
2.5(3) = 7.5

24. Find the measures of all missing angles in the rhombus.
1 = 78- diagonal bisects the angles. 2 = 90- diagonals are Perpendicular. 3 = 12- sum of the interior angles of a triangle is 180. 4= 78- opposite angles are congruent.

25. Try: Find all the measured angles in the rhombus
1 = 90- diagonals are perpendicular 2 = 50- diagonals the angles 3 = 50 opposite angles are congruent 4 = 40 sum of the interior angles of a triangle is 180

26. Find the length of the diagonal.
8x + 2 = 5x + 11
3x + 2 =
3x =
X = 3
8(3) +2 = 26
5(3) +11 = both diagonals are 26 units

27. 5y – 9 = y +5 4y – 9 = 5 4y = 14 y = 7/2 or = 8.5 units 5(3.5) – 9 = 8.5 units diagonals are 8.5 units

28. 6-6 Placing figures in the Coordinate Plane
To name coordinates of special figures by using their properties.

29. Find coordinate B for the parallelogram below.
Since it is a parallelogram, It must have the same y-coordinate q. The x- coordinate is –x-p Therefore, B(-x-p,q)

30. Find the coordinate Q for the parallelogram below.
Q(b+s, c)

31. What did you learn today? What is still confusing?
Review Unit test Summative
What did you learn today?
What is still confusing?