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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

3. Arcs and Chords

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Exercise 14 Page 737

By Congruent Corresponding Chords Theorem in the same circle two minor arcs are congruent if and only if their corresponding chords are congruent.

11

Practice makes perfect

We will find the value of x. Notice that these circles are congruent according to the exercise.

The sum of the minor and major arc of the same chord is 360^(∘). With this information, we can write an equation that contains mTU.

205^(∘) +mTU=360^(∘) ⇕ mTU=155^(∘) Since the minor arcs of the chords are congruent, we can use the Congruent Corresponding Chords Theorem.

Congruent Corresponding Chords Theorem
In congruent circles two minor arcs are congruent if and only if their corresponding chords are congruent.

We know that two minor arcs RS and TU are congruent. By the theorem the corresponding chords are also congruent. 3x=7x-44 Let's solve this equation for x.

3x=7x-44

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Solve for x

LHS-3x=RHS-3x

0=4x-44

LHS+44=RHS+44

44=4x

.LHS /4.=.RHS /4.

11=x

Rearrange equation

x=11

Subchapter links

Exercises p.736-740