1. anonymous

2. anonymous

The diagonals intersect at right angles and bisect the corners of the square.|dw:1443056876414:dw|

3. anonymous

oh okay

4. anonymous

for the rhombus, all sides are always congruent, so that's the 4th and 6th. diagonals aren't necessarily congruent, so not the 5th. the third b/c diagonals bisect corners. opposite angles are congruent so the 1st but not the 2nd.

5. anonymous

okay i still dont get it @peachpi

6. anonymous

@Mertsj do you get it?

7. Mertsj

yes

8. anonymous

can you explain it?

9. Mertsj

The figure is a square. All the sides are equal. The angles of the square and all right angles. The diagonals bisect the angles of the square and so they are all 45 degrees. The diagonals bisect each other and the diagonals are congruent.

10. Mertsj

|dw:1443059225044:dw|

11. Mertsj

|dw:1443059348234:dw|

12. anonymous

oh okay

13. Mertsj

|dw:1443059475757:dw|

14. Mertsj

|dw:1443059540994:dw|

15. anonymous

so this shape above is for the 2nd question?

16. Mertsj

|dw:1443059602046:dw|

17. Mertsj

Yes. The second question is about a rhombus.

18. anonymous

19. anonymous

im so lost

20. Mertsj

Do you know what a square is?

21. anonymous

yes

22. Mertsj

Do you know that all the sides of a square are equal?

23. anonymous

yes

24. Mertsj

Do you know what a diagonal of a square is?

25. anonymous

not so much

26. Mertsj

|dw:1443059854717:dw|

27. Mertsj

|dw:1443059900268:dw|

28. anonymous

oh okay got ya

29. Mertsj

|dw:1443059966447:dw|

30. Mertsj

Do you know that diagonals of a square are equal?

31. anonymous

yes i do

32. Mertsj

33. anonymous

hk = gj ?

34. Mertsj

You must name the segments the way they are labelled and they are labelled using capital letters.

35. anonymous

HK = GJ ?

36. Mertsj

yes.

37. Mertsj

Do you know what perpendicular means?

38. anonymous

m<KLJ = m<HLJ ? and yes i do

39. Mertsj

yes

40. Mertsj

Do you know that the diagonals of a square bisect the angles?

41. anonymous

um sorta

42. Mertsj

Do you know what bisect means?

43. anonymous

m<HJG = m<GKJ?

44. anonymous

yes

45. Mertsj

yes that is correct for number3

46. Mertsj

Do you know what perimeter is?

47. anonymous

yes i do

48. Mertsj

49. anonymous

50. Mertsj

How many sides does a triangle have?

51. anonymous

3

52. Mertsj

What are the three sides of triangle HJK?

53. anonymous

2

54. anonymous

12?

55. Mertsj

The three sides are HJ and JK and HK

56. Mertsj

How long is HJ ?

57. anonymous

2?

58. Mertsj

How long is JK?

59. anonymous

2

60. Mertsj

How long is HK?

61. anonymous

2

62. Mertsj

how long is GL?

63. anonymous

2

64. Mertsj

Look at the picture. Clearly GH and GL are not labelled with the same number.

65. anonymous

$\sqrt{2}$

66. anonymous

which is 1.41

67. anonymous

right

68. Mertsj

Use the exact value. How long is KL ?

69. anonymous

$\sqrt{2}$

70. Mertsj

How long is KH?

71. anonymous

i dont know how to figure that out

72. Mertsj

$\sqrt{2}+\sqrt{2}=2\sqrt{2}$

73. Mertsj

Now find the perimeter of triangle HJK

74. anonymous

um

75. Mertsj

HJ +JK +HK = $2+2+ 2\sqrt{2}=4+2\sqrt{2}$

76. Mertsj

And that is the perimeter.

77. anonymous

uhh

78. Mertsj

What does uhh mean???

79. anonymous

i dont know how to solve that

80. Mertsj

Solve what?

81. anonymous

so thats the perimeter the 2 + 2+ 2 equation

82. Mertsj

$4+2\sqrt{2}$ is the perimeter and that is what the problem asked you to find.

83. anonymous

oh okay

84. anonymous

85. Mertsj

The second figure is a rhombus. Do you know what that means?

86. anonymous

i know what a rhombus is

87. Mertsj

What is it?

88. anonymous

its a parallelogram with opposite acute angles from what i remember

89. Mertsj

A rhombus is a parallelogram which has 4 equal sides.

90. Mertsj

So you need to know some stuff about a parallelogram.

91. anonymous

i know that

92. Mertsj

In a parallelogram, the opposite sides and parallel and the opposite angles are congruent and the consecutive angles are supplementary.

93. Mertsj

Do you know all that stuff?

94. anonymous

yup sure do

95. Mertsj

The diagonals of a parallelogram form a transversal between the parallel sides. Do you know that?

96. anonymous

its just when i do the check all that applies i can never really catch which ones are different

97. anonymous

okay

98. Mertsj

If two parallel lines are cut by the transversal, the alternate interior angles are congruent. Do you know that?

99. Mertsj

|dw:1443061913872:dw|

100. Mertsj

|dw:1443061950637:dw|

101. Mertsj

That means that angle 1 is congruent to angle 2

102. anonymous

oh alright

103. Mertsj

|dw:1443061999682:dw|

104. anonymous

so A is congruent to C

105. Mertsj

|dw:1443062058029:dw|

106. Mertsj

yes. Angle A is congruent to Angle C

107. anonymous

so i check ABD is congruent CBD

108. Mertsj

On what basis do you say that?

109. anonymous

because of the picture about there all congruent to each other no?

110. Mertsj

|dw:1443062227396:dw|

111. anonymous

ohh okay i guess not

112. anonymous

so AC = BD

113. Mertsj

That is one of the things these two problems is trying to teach you: In a square, the diagonals bisect the angles but not in a rhombus.

114. anonymous

oh

115. Mertsj

That is another thing these two problems show: In a square the diagonals are congruent but not in a rhombus.

116. anonymous

i guess

117. Mertsj

But AB does equal BC because all the sides of a rhombus are congruent.

118. anonymous

so the 2nd and 3rd bullet dont make sense so they dont apply

119. Mertsj

So which ones are you going to check?

120. anonymous

so far the 1st and the 4th

121. Mertsj

Not the 5th one right?

122. anonymous

and i think the 5th one applies

123. anonymous

not the 6th one

124. Mertsj

What are AC and BD called?

125. anonymous

3 and 4 ? or i dont know

126. Mertsj

|dw:1443062676347:dw|

127. anonymous

so its Diagonal got ya

128. Mertsj

|dw:1443062765075:dw|

129. anonymous

so wouldnt that one apply

130. Mertsj

No.

131. Mertsj

132. anonymous

no i dont believe that one applies

133. Mertsj

134. Mertsj

AD is a side of the rhombus

135. Mertsj

What is CD?

136. anonymous

okay and so is DC

137. anonymous

*CD

138. Mertsj

And what do you know about the sides of a rhombus?

139. anonymous

all sides are equal

140. anonymous

so 1,4 and 6 apply correct?

141. Mertsj

I would say so but now here is a technicality to consider and you will have to make a judgment call based upon what you know about your teacher.

142. Mertsj

|dw:1443063106522:dw|

143. anonymous

oh okay

144. Mertsj

|dw:1443063191291:dw|

145. Mertsj

So you see that technically, 4 and 6 should have the lines over the top of the letters to indicate that they are segments. But I don't know if that is important to your teacher in this context or not. What do you think?

146. anonymous

ehh i dont think she'll mind if i explain that to her she will be okay with what we choose

147. Mertsj

That would be the sensible thing.

148. anonymous

thank you so much i appreciate it

149. Mertsj

You're welcome.