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Chapter 10: Problem 51

If the ratio of the corresponding sides of two similar triangles is 1 to \(1\left(\frac{1}{1}\right)\), what must be true about the triangles?

Short Answer

Expert verified
The two triangles are not only similar but also congruent.

Step by step solution

01

Understanding Similarity

Similarity in triangles is defined as the condition in which two triangles have the same shape but not necessarily the same size. This means that their corresponding angles are equal and the lengths of their corresponding sides are proportional.
02

Recognizing the Ratio of Corresponding Sides

The ratio of the corresponding sides of the two triangles is given as \(1\left(\frac{1}{1}\right)\). The ratio of corresponding sides is the same for similar triangles.
03

Concluding What the Ratio Implies

When the ratio of the corresponding sides of two similar triangles is \(1\left(\frac{1}{1}\right)\), this signifies that the lengths of each pair of corresponding sides are the same. Therefore, the triangles must not only be similar but also congruent.

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Most popular questions from this chapter

A police helicopter is flying at 800 feet. A stolen car is sighted at an angle of depression of \(72^{\circ}\). Find the distance of the stolen car, to the nearest foot, from a point directly below the helicopter.

The measure of the angle is three times greater than its supplement.

Use similar triangles to solve Exercises 37-38. A person who is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86 -foot shadow. The person's shadow is 6 feet in length. What is the tree's height?

The measure of the angle is \(81^{\circ}\) more than twice that of its supplement.

What are supplementary angles? Describe how to find the measure of an angle's supplement.
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