AB ≅ CD. Find the length of BD.?

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In summary, AB ≅ CD means that line segment AB is congruent to line segment CD, and they have the same length. The lengths of AB and CD can be determined by measuring or using geometric tools. BD represents the length of the line segment connecting AB and CD, and it can be found using the average of the lengths of AB and CD. Even if the lengths of AB and CD are not known, they can be found using geometric tools or mathematical formulas to determine the length of BD.
  • #1
Leo34005
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Homework Statement



AB ≅ CD. Find the length of BD.?

img42.gif


AB ≅ CD. Find the length of BD.


Homework Equations




A) 8
B) 10
C) 4
D) 7
E) -7



The Attempt at a Solution




AB = 2x + 5x + 7 = 7x + 7

CD = 5x + 7 + 3x - 4 = 8x + 3

AB ~= CD
7x + 7 = 8x + 3

7 - 3 = 8x - 7x => x = 4

BD = 3x - 4 = 3(4) - 4 = 8

ans: A) 8
 
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  • #2
correct. good job
 

1. What does AB ≅ CD mean?

AB ≅ CD means that line segment AB is congruent to line segment CD, meaning they have the same length.

2. How do you know that AB and CD are congruent?

In order for two line segments to be congruent, they must have the same length. This can be determined by measuring the length of each line segment or by using geometric tools such as a compass and straightedge to create congruent segments.

3. What does BD represent in this scenario?

BD represents the length of the line segment connecting the two congruent segments AB and CD. It is the length we are trying to find in this problem.

4. Can you find the length of BD without knowing the lengths of AB and CD?

Yes, because AB and CD are congruent, we can use the properties of congruent line segments to know that the length of BD is equal to the length of either AB or CD. This is because congruent line segments have equal measurements.

5. How can you use this information to find the length of BD?

If we know the lengths of AB and CD, we can simply find the average of the two lengths to determine the length of BD. If we do not know the lengths of AB and CD, we can use geometric tools or mathematical formulas to find their lengths, and then use the average to determine the length of BD.

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