1. Please read the following and consider yourself in it.
An Affirmation
Please read the following and consider yourself in it.
I am capable of learning. I can accomplish mathematical tasks. I am ultimately responsible for my learning.

2. Unit Objectives
G.GPE.5- SWBAT apply properties of similar triangles IOT prove slope criteria for parallel and perpendicular lines.
G.GPE.5-SWBAT apply slope criteria for parallel and perpendicular lines IOT find the equation of a line parallel or perpendicular to a given line that passes through a given point.
G.GPE.4 SWBAT apply distance formula, partition formula and slope criteria IOT prove geometric theorems on quadrilaterals and polygons algebraically.
G.GPE.7- SWBAT apply algebraic methods on coordinates IOT to compute perimeters of polygons and areas of rectangles and triangles.

3. Review Activity for Equations of Lines
Classify the lines as parallel, perpendicular or neither with respects to each other:
a. 2x + 3y =5, 3x + 2y = 7
b. x –y =4, x -2y = 3
c. x+2y = 5, x-y = 0
1. Find the equation of the line parallel to 3x-2y =5 and passing through (3, -2)
2. Find the equation of the perpendicular bisector of the line joining the points (3, -2) and ( 5, 4)
3. Find the equation of the line parallel to x =3 and passing through (5,-1)
4. Find the equation of the line perpendicular to x =3 and passing through (5,-1)
Lesson Menu

4. LMNO is a rhombus. Find x.
A. 5
B. 7
C. 10
D. 12
5-Minute Check 1

5. LMNO is a rhombus. Find x.
A. 5
B. 7
C. 10
D. 12
5-Minute Check 1

6. LMNO is a rhombus. Find y. A. 6.75 B. 8.625 C. 10.5 D. 12
5-Minute Check 2

7. LMNO is a rhombus. Find y. A. 6.75 B. 8.625 C. 10.5 D. 12
5-Minute Check 2

8. QRST is a square. Find n if mTQR = 8n + 8.
B. 9 C
D. 6.5
5-Minute Check 3

9. QRST is a square. Find n if mTQR = 8n + 8.
B. 9 C
D. 6.5
5-Minute Check 3

10. QRST is a square. Find w if QR = 5w + 4 and RS = 2(4w – 7).
B. 5
C. 4
D. 3.3 _
5-Minute Check 4

11. QRST is a square. Find w if QR = 5w + 4 and RS = 2(4w – 7).
B. 5
C. 4
D. 3.3 _
5-Minute Check 4

12. QRST is a square. Find QU if QS = 16t – 14 and QU = 6t + 11.
B. 10
C. 54
D. 65
5-Minute Check 5

13. QRST is a square. Find QU if QS = 16t – 14 and QU = 6t + 11.
B. 10
C. 54
D. 65
5-Minute Check 5

14. Which statement is true about the figure shown, whether it is a square or a rhombus?
C. JM║LM D.
5-Minute Check 6

15. Which statement is true about the figure shown, whether it is a square or a rhombus?
C. JM║LM D.
5-Minute Check 6

16. Mathematical Practices
Content Standards
G.GPE.4 Use coordinates to prove simple geometric theorems algebraically.
G.MG.3 Apply geometric methods to solve problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).
Mathematical Practices
1 Make sense of problems and persevere in solving them.
2 Reason abstractly and quantitatively.
CCSS

17. You used properties of special parallelograms.
Apply properties of trapezoids.
Apply properties of kites.
Then/Now

18. midsegment of a trapezoid kite
bases
legs of a trapezoid
base angles
isosceles trapezoid
midsegment of a trapezoid
kite
Vocabulary

19. Concept 1

20. Concept 2

21. Use Properties of Isosceles Trapezoids
A. BASKET Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and LN = 3.6 feet, find mMJK.
Example 1A

22. Since JKLM is a trapezoid, JK║LM.
Use Properties of Isosceles Trapezoids
Since JKLM is a trapezoid, JK║LM.
mJML + mMJK = 180 Consecutive Interior Angles Theorem
130 + mMJK = 180 Substitution
mMJK = 50 Subtract 130 from each side.
Answer:
Example 1A

23. Since JKLM is a trapezoid, JK║LM.
Use Properties of Isosceles Trapezoids
Since JKLM is a trapezoid, JK║LM.
mJML + mMJK = 180 Consecutive Interior Angles Theorem
130 + mMJK = 180 Substitution
mMJK = 50 Subtract 130 from each side.
Answer: mMJK = 50
Example 1A

24. Use Properties of Isosceles Trapezoids
B. BASKET Each side of the basket shown is an isosceles trapezoid. If mJML = 130, KN = 6.7 feet, and JL is 10.3 feet, find MN.
Example 1B

25. JL = KM Definition of congruent JL = KN + MN Segment Addition
Use Properties of Isosceles Trapezoids
Since JKLM is an isosceles trapezoid, diagonals JL and KM are congruent.
JL = KM Definition of congruent
JL = KN + MN Segment Addition
10.3 = MN Substitution
3.6 = MN Subtract 6.7 from each side.
Answer:
Example 1B

26. JL = KM Definition of congruent JL = KN + MN Segment Addition
Use Properties of Isosceles Trapezoids
Since JKLM is an isosceles trapezoid, diagonals JL and KM are congruent.
JL = KM Definition of congruent
JL = KN + MN Segment Addition
10.3 = MN Substitution
3.6 = MN Subtract 6.7 from each side.
Answer: MN = 3.6
Example 1B

27. A. Each side of the basket shown is an isosceles trapezoid
A. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and IG = 4.3 feet, find mEFG.
A. 124
B. 62
C. 56
D. 112
Example 1A

28. A. Each side of the basket shown is an isosceles trapezoid
A. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and IG = 4.3 feet, find mEFG.
A. 124
B. 62
C. 56
D. 112
Example 1A

29. B. Each side of the basket shown is an isosceles trapezoid
B. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and EG = 14.1 feet, find IH.
A. 4.3 ft
B. 8.6 ft
C. 9.8 ft
D ft
Example 1B

30. B. Each side of the basket shown is an isosceles trapezoid
B. Each side of the basket shown is an isosceles trapezoid. If mFGH = 124, FI = 9.8 feet, and EG = 14.1 feet, find IH.
A. 4.3 ft
B. 8.6 ft
C. 9.8 ft
D ft
Example 1B

31. Isosceles Trapezoids and Coordinate Geometry
Quadrilateral ABCD has vertices A(5, 1), B(–3, –1), C(–2, 3), and D(2, 4). Show that ABCD is a trapezoid and determine whether it is an isosceles trapezoid.
A quadrilateral is a trapezoid if exactly one pair of opposite sides are parallel. Use the Slope Formula.
Example 2

32. slope of slope of slope of Answer:
Isosceles Trapezoids and Coordinate Geometry
slope of
slope of
slope of
Answer:
Example 2

33. slope of slope of slope of
Isosceles Trapezoids and Coordinate Geometry
slope of
slope of
slope of
Answer: Exactly one pair of opposite sides are parallel, So, ABCD is a trapezoid.
Example 2

34. Use the Distance Formula to show that the legs are congruent.
Isosceles Trapezoids and Coordinate Geometry
Use the Distance Formula to show that the legs are congruent.
Answer:
Example 2

35. Use the Distance Formula to show that the legs are congruent.
Isosceles Trapezoids and Coordinate Geometry
Use the Distance Formula to show that the legs are congruent.
Answer: Since the legs are not congruent, ABCD is not an isosceles trapezoid.
Example 2

36. A. trapezoid; not isosceles B. trapezoid; isosceles C. not a trapezoid
Quadrilateral QRST has vertices Q(–1, 0), R(2, 2), S(5, 0), and T(–1, –4). Determine whether QRST is a trapezoid and if so, determine whether it is an isosceles trapezoid.
A. trapezoid; not isosceles
B. trapezoid; isosceles
C. not a trapezoid
D. cannot be determined
Example 2

37. A. trapezoid; not isosceles B. trapezoid; isosceles C. not a trapezoid
Quadrilateral QRST has vertices Q(–1, 0), R(2, 2), S(5, 0), and T(–1, –4). Determine whether QRST is a trapezoid and if so, determine whether it is an isosceles trapezoid.
A. trapezoid; not isosceles
B. trapezoid; isosceles
C. not a trapezoid
D. cannot be determined
Example 2

38. Concept 3

39. Midsegment of a Trapezoid
In the figure, MN is the midsegment of trapezoid FGJK. What is the value of x?
Example 3

40. Trapezoid Midsegment Theorem
Midsegment of a Trapezoid
Read the Test Item
You are given the measure of the midsegment of a trapezoid and the measures of one of its bases. You are asked to find the measure of the other base.
Solve the Test Item
Trapezoid Midsegment Theorem
Substitution
Example 3

41. Subtract 20 from each side.
Midsegment of a Trapezoid
Multiply each side by 2.
Subtract 20 from each side.
Answer:
Example 3

42. Subtract 20 from each side.
Midsegment of a Trapezoid
Multiply each side by 2.
Subtract 20 from each side.
Answer: x = 40
Example 3

43. WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ = 25.
A. XY = 32
B. XY = 25
C. XY = 21.5
D. XY = 11
Example 3

44. WXYZ is an isosceles trapezoid with median Find XY if JK = 18 and WZ = 25.
A. XY = 32
B. XY = 25
C. XY = 21.5
D. XY = 11
Example 3

45. Concept 4

46. A. If WXYZ is a kite, find mXYZ.
Use Properties of Kites
A. If WXYZ is a kite, find mXYZ.
Example 4A

47. mW + mX + mY + mZ = 360 Polygon Interior Angles Sum Theorem
Use Properties of Kites
Since a kite only has one pair of congruent angles, which are between the two non-congruent sides, WXY  WZY. So, WZY = 121.
mW + mX + mY + mZ = 360 Polygon Interior Angles Sum Theorem
mY = 360 Substitution
mY = 45 Simplify.
Answer:
Example 4A

48. mW + mX + mY + mZ = 360 Polygon Interior Angles Sum Theorem
Use Properties of Kites
Since a kite only has one pair of congruent angles, which are between the two non-congruent sides, WXY  WZY. So, WZY = 121.
mW + mX + mY + mZ = 360 Polygon Interior Angles Sum Theorem
mY = 360 Substitution
mY = 45 Simplify.
Answer: mXYZ = 45
Example 4A

49. B. If MNPQ is a kite, find NP.
Use Properties of Kites
B. If MNPQ is a kite, find NP.
Example 4B

50. NR2 + MR2 = MN2 Pythagorean Theorem (6)2 + (8)2 = MN2 Substitution
Use Properties of Kites
Since the diagonals of a kite are perpendicular, they divide MNPQ into four right triangles. Use the Pythagorean Theorem to find MN, the length of the hypotenuse of right ΔMNR.
NR2 + MR2 = MN2 Pythagorean Theorem
(6)2 + (8)2 = MN2 Substitution
= MN2 Simplify.
100 = MN2 Add.
10 = MN Take the square root of each side.
Example 4B

51. Since MN  NP, MN = NP. By substitution, NP = 10.
Use Properties of Kites
Since MN  NP, MN = NP. By substitution, NP = 10.
Answer:
Example 4B

52. Since MN  NP, MN = NP. By substitution, NP = 10.
Use Properties of Kites
Since MN  NP, MN = NP. By substitution, NP = 10.
Answer: NP = 10
Example 4B

53. A. If BCDE is a kite, find mCDE.
Example 4A

54. A. If BCDE is a kite, find mCDE.
Example 4A

55. B. If JKLM is a kite, find KL.
C. 7
D. 8
Example 4B

56. B. If JKLM is a kite, find KL.
C. 7
D. 8
Example 4B

57. End of the Lesson