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2 years ago

In the figure, ∆ABD ≅ ∆CBD by Angle-Side-Angle (ASA). Which segments are congruent by CPCTC?

Mathematics

1 answer:

Elis [28]2 years ago

8 0

Answer: AB ≅ CB

Step-by-step explanation:

In the given figure, we have ∆ABD ≅ ∆CBD

The CPCTC property of congruent triangles says that if two triangles are congruent then their corresponding parts ( angles and segments ) are congruent.

Since we have given that ∆ABD ≅ ∆CBD.

Therefore, the corresponding segments are congruent.

As segment AB is corresponding to segment CB. [First two letters]

Therefore, segment AB is congruent to segment CB.

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30 years ago zoe was 2/3 as old as luke, 18 years ago zoe was 5/6 as old as luke how old are they now

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Based on the mathematical statements, Zoe is 56 years old and Luke is 66 years old, now

<h3>How to determine how old they are now?</h3>

From the question, we have the following statements that can be used in our computation:

30 years ago

Zoe was 2/3 as old as Luke

18 years ago

Zoe was 5/6 as old as Luke

Let their present ages be represented as

Zoe = x

Luke = y

So, we have the following representations

30 years ago

Zoe was 2/3 as old as Luke

x - 36 = 2/3(y - 36)

18 years ago

Zoe was 5/6 as old as Luke

x - 18 = 5/6(y - 18)

So, we have the following system of equations

x - 36 = 2/3(y - 36)

x - 18 = 5/6(y - 18)

Make x the subject in x - 18 = 5/6(y - 18)

x = 5/6(y - 18) + 16

Substitute x = 5/6(y - 18) + 16 in x - 36 = 2/3(y - 36)

5/6(y - 18) + 16 - 36 = 2/3(y - 36)

Open the brackets

5/6y - 15 + 16 - 36 = 2/3y - 24

Evaluate the like terms

5/6y - 35 = 2/3y - 24

Multiply through by 6

5y - 210 = 4y - 144

Evaluate the like terms

y = 66

Substitute y = 66 in x = 5/6(y - 18) + 16

x = 5/6(66 - 18) + 16

Evaluate

x = 56

Recall that

Zoe = x

Luke = y

So, we have

Zoe = x = 56

Luke = y = 66

Hence, they are 56 and 66 years, now