If we have a kite ABCD where AB = CD and DC = CA.
Let E be a midpoint between BC
Since triangle ABC is an isosceles triangle, ray BE bisects angle ABC and is perpendicular to AC.
So, angle ABE = CBE.
<span>Since also triangle CDA is isosceles, line DE is perpendicular to AC for the same reason. Therefore, AC is perpendicular to BD.</span>
Answers:
x = 5/2 = 2.5
y = 10
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Explanation:
Focus on the smallest triangle and the medium sized triangle. We can form the proportion 2/4 = x/5 by dividing the corresponding sides together.
Solving for x leads us to the following
2/4 = x/5
2*5 = 4*x
10 = 4x
4x = 10
x = 10/4
x = 5/2
x = 2.5
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Now focus on the medium sized triangle and the largest triangle. We'll use the same idea as before
4/8 = 5/y
4y = 8*5
4y = 40
y = 40/4
y = 10
Note how each horizontal line is a midsegment, which means that jumping from y = 10 to 5 is us taking half of that value. Then going from 5 to x = 5/2 = 2.5 is another step of cutting in half.
I saw the pie chart that should have accompanied this word problem.
Favorite fruit:
Grapes = 150
Apple = 220
Orange = 185
Banana = 235
Choices:
A) 37/47
B) 185/790
C) 790/275
D) 235/185
Oranges = 185 ; Bananas = 235
Ratio of oranges to Bananas = 185/235
Simplify 185/235
185 ÷ 5 = 37
235 ÷ 5 = 47
Ratio of oranges to Bananas = 37/47 Choice A.
9(10+x)
To apply the distributive property, we need to multiply the number out of the parenthesis by each number inside.
9*10 = 90
9*x = 9x
9x + 90
Final answer: 9x + 90