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9.16: Corresponding Parts of Congruent Figures

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Have you ever had to do a project with a partner where one of you does one part and the other does the other? Well, Sam and Allison are working on just that task.

Sam has drawn two parallelograms. He measured them carefully and told Allison that the two parallelograms will create a "launch pad" for the skateboard park. He isn't sure his design will work, but he has this idea of putting one parallelogram on the ground, then put four springs in the middle and finally put the other parallelogram on top.

"I think you are crazy," Allison told him when she heard his idea.

"That doesn't matter, we were asked to come up with a unique idea and it is unique," Sam responded.

"Okay, so I have to match up the sides right?"

"Yes, only the corresponding sides," Sam said walking away.

Allison looked at the two parallelograms for Sam's design. She knows that she needs to write out the corresponding sides, but she isn't sure how to do it.

That is where you come in. This Concept is all about corresponding parts of congruent figures. Pay attention and you will be ready at the end of the Concept.

Guidance

Now that you understand the difference between congruent figures and similar figures, we can look at the corresponding parts of congruent triangles.

The word corresponding refers to parts that match between two congruent triangles. We can identify corresponding angles and corresponding sides.

First, we can name the corresponding angles. Corresponding angles are matching angles between the two triangles. Corresponding angles will have the same measure in congruent triangles.

\angle{A} \cong \angle{D} \\\angle{B} \cong \angle{E} \\\angle{C} \cong \angle{F}

Here the angles are connected with the symbol for congruent. When you see the equals sign with a squiggly line on top, you know that the items on each side of the equation are congruent.

Next, we can name the corresponding sides. Corresponding sides are matching sides between two triangles. They will have the same length in congruent triangles.

\overline{AB} \cong \overline{DE} \\\overline{AC} \cong \overline{DF} \\\overline{BC} \cong \overline{EF}

Use the following diagram of two congruent triangles to answer each question.

Example A

Angle E is congruent to angle _____

Solution: H

Example B

\overline{FG} \cong \underline{\;\;\;\;\;\;\;\;\;\;\;}

Solution: \overline{IJ}

Example C

Angle J is congruent to angle _____

Solution: G

Now back to Allison's dilemma. Here is the original problem once again.

Sam has drawn two parallelograms. He measured them carefully and told Allison that the two parallelograms will create a "launch pad" for the skateboard park. He isn't sure his design will work, but he has this idea of putting one parallelogram on the ground, then put four springs in the middle and finally put the other parallelogram on top.

"I think you are crazy," Allison told him when she heard his idea.

"That doesn't matter, we were asked to come up with a unique idea and it is unique," Sam responded.

"Okay, so I have to match up the sides right?"

"Yes, only the corresponding sides," Sam said walking away.

Allison looked at the two parallelograms for Sam's design. She knows that she needs to write out the corresponding sides, but she isn't sure how to do it.

To accomplish this task, Allison will need to turn the parallelograms in her mind so that they are both in the same position. Once this has been done, she can write the following pairs of corresponding sides.

\overline{AD} \cong \overline{PS} \\\overline{AB} \cong \overline{PQ} \\\overline{BC} \cong \overline{QR} \\ \overline{DC} \cong \overline{SR}

This is the answer.

Vocabulary

Here are the vocabulary words in this Concept.

Congruent
having the same size and shape and measurement
Similar
having the same shape, but not the same size. Similar shapes are proportional to each other.
Corresponding
matching-corresponding sides between two triangles are sides that match up

Guided Practice

Here is one for you to try on your own.

These two figures are congruent.Which angle is congruent to angle A?

Answer

Because you have been told that these two figures are congruent, it is important not to let the fact that they are in a different position throw you off. In your mind you will need to turn the second figure so that it is in the same position as the first one. If this is difficult for you to visualize, you can also re - draw the figure.

Here is the answer.

\angle{A} \cong \angle{P}

Video Review

Here are videos for review.

Khan Academy Congruent and Similar Triangles

James Sousa, Congruent and Similar Triangles

Practice

Directions: Use the following triangles to answer the questions.

1. Are these two triangles similar or congruent?

2. How do you know?

3. Side DE is congruent to which other side?

4. Side DF is congruent to which other side?

5. Side EF is congruent to which other side?

6. If the side length of DE is 10, what is the side length of GH ?

7. If the side length of HI is 8, which other side is also 8?

Directions: Use the following figures to answer the questions.

8. These two figures are congruent. Explain two ways that you can determine whether or not figures are congruent.

9. Angle Q is congruent to which other angle?

10. Angle R is congruent to which other angle?

11. Angle S is congruent to which other angle?

12. If PQ is 7 cm, which other sides are 7 cm?

13. If QR is 4 cm, which other sides are 4 cm?

14. If Angle D is 70 degrees, name another 70 degree angle.

15. If Angle A is 110 degrees, name another 110 degree angle.

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Date Created:

Oct 29, 2012

Last Modified:

Aug 18, 2014
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