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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 2 Page 736

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

70

Practice makes perfect

We will find the value of x. Examining the diagram, we immediately notice that the chords FG and HG are congruent.

Let's recall the Congruent Corresponding Chords Theorem.

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

We know that chords FG and HG are congruent. By the theorem, the corresponding minor arcs are also congruent. mFG=mHG Since mHG equals x it must means that FG also equals x. By the Arc Addition Postulate and feature of the circle all central angles sum up to 360^(∘). 220^(∘)+x^(∘)+x^(∘)=360^(∘) Let's solve this equation for x.

220^(∘)+x^(∘)+x^(∘)=360^(∘)

▼

Solve for x^(∘)

Add terms

220^(∘)+2x^(∘)=360^(∘)

LHS-220^(∘)=RHS-220^(∘)

2x^(∘)=140^(∘)

.LHS /2.=.RHS /2.

x^(∘)=70^(∘)

Subchapter links

Exercises p.736-740