Calculate Rectangle Perimeter Using Congruent Triangles: 6 and 8 Unit Measures

Q: How do I know which sides correspond in congruent triangles?

Look at the order of vertices in the congruence statement! In $ \triangle BCE \cong \triangle FED $, the first letters (B and F) correspond, second letters (C and E) correspond, and third letters (E and D) correspond.

Q: Why is ED = BC = 6 and not one of the other sides?

From $ \triangle BCE \cong \triangle FED $, vertex C corresponds to vertex E, and vertex E corresponds to vertex D. So side BC corresponds to side FE, and side CE corresponds to side ED. Since BC = 6, we get FE = 6, not ED = 6.

Q: How do I find the other dimension of the rectangle?

Look at the diagram! The side EF is marked as 8, and since EDGF is a rectangle, opposite sides are equal. So EF = DG = 8, making the rectangle dimensions 6 × 8.

Q: What's the perimeter formula for a rectangle again?

Perimeter = 2 × (length + width). Since rectangles have two pairs of equal sides, you add length + width once, then multiply by 2 to account for both pairs.

Q: Can I just add all four sides instead?

Absolutely! For rectangle EDGF: ED + DG + GF + FE = 6 + 8 + 6 + 8 = 28. Both methods give the same answer, so use whichever feels easier to you!

Congruent Triangles with Rectangle Perimeter

ΔBCE≅ΔFED

Calculate the perimeter of the rectangle EDGF.

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Step-by-step video solution

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00:00 Determine the perimeter of the rectangle EDFG

00:03 The triangles are congruent according to the given data

00:10 The sides are equal according to the theory of congruence

00:13 Substitute in the relevant values according to the given data

00:19 Opposite sides in the rectangle are equal

00:28 The perimeter of the rectangle equals the sum of its sides

00:37 Substitute in the relevant values and solve to find the perimeter

01:06 This is the solution

Step-by-step written solution

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Understand the problem

ΔBCE≅ΔFED

Calculate the perimeter of the rectangle EDGF.

Step-by-step solution

To find the perimeter of rectangle EDGF, we will follow these steps:

Step 1: Recognize congruence $\Delta BCE \equiv \Delta FED$ .
Step 2: Use congruent triangles to find side lengths of ED and DF.
Step 3: Calculate the perimeter using the formula for rectangles.

Now, let's proceed with the solution:

Step 1: Given $\Delta BCE$ and $\Delta FED$ are congruent triangles, their corresponding sides are equal. Thus, since $BC = 6$ , it follows that $ED = BC = 6$ .

Step 2: From the configuration of the rectangle, note that $FE$ (same as AE) is given to be 8, hence $GF = 8$ because EDGF is a rectangle.

Step 3: The perimeter of rectangle EDGF can be calculated using:

P = 2 \times (\text{Length} + \text{Width}) = 2 \times (ED + DF) = 2 \times (6 + 8) = 28

Therefore, the solution to the problem is that the perimeter of rectangle EDGF is 28.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Congruence Rule: Corresponding sides of congruent triangles are equal lengths
Technique: Use $\triangle BCE \cong \triangle FED$ to find ED = BC = 6
Check: Rectangle perimeter = 2(length + width) = 2(6 + 8) = 28 ✓

Common Mistakes

Avoid these frequent errors

Confusing corresponding sides in congruent triangles
Don't assume any side equals any other side = wrong measurements! Triangle congruence means specific sides correspond to specific sides. Always identify which vertices match up in the congruence statement $\triangle BCE \cong \triangle FED$ to find correct corresponding sides.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle below.

Side DC has a length of 1.5 cm and side AD has a length of 9.5 cm.

What is the perimeter of the rectangle?

FAQ

Everything you need to know about this question

How do I know which sides correspond in congruent triangles?

Look at the order of vertices in the congruence statement! In $\triangle BCE \cong \triangle FED$ , the first letters (B and F) correspond, second letters (C and E) correspond, and third letters (E and D) correspond.

Why is ED = BC = 6 and not one of the other sides?

From $\triangle BCE \cong \triangle FED$ , vertex C corresponds to vertex E, and vertex E corresponds to vertex D. So side BC corresponds to side FE, and side CE corresponds to side ED. Since BC = 6, we get FE = 6, not ED = 6.

How do I find the other dimension of the rectangle?

Look at the diagram! The side EF is marked as 8, and since EDGF is a rectangle, opposite sides are equal. So EF = DG = 8, making the rectangle dimensions 6 × 8.

What's the perimeter formula for a rectangle again?

Perimeter = 2 × (length + width). Since rectangles have two pairs of equal sides, you add length + width once, then multiply by 2 to account for both pairs.

Can I just add all four sides instead?

Absolutely! For rectangle EDGF: ED + DG + GF + FE = 6 + 8 + 6 + 8 = 28. Both methods give the same answer, so use whichever feels easier to you!

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