Exercise 34 Page 383

Angle	Measure
∠ JML	60^(∘)
∠ KJM	120^(∘)
∠ KLM	120^(∘)

Practice makes perfect

a Let's take a look at the diagram. We are given that JK=LM= 21 feet and KL=JM= 9 feet. We will focus on only one parking space.

As we can see both pairs of opposite sides of this quadrilateral are congruent, so this figure is a parallelogram by the Parallelogram Opposite Sides Converse.

b In this part we want to find the measures of ∠ JML, ∠ KJM, and ∠ KLM knowing that m∠ JKL= 60^(∘). Let's look at the diagram. Again we will focus on only one parking space.

Since in the previous part we showed that JKLM is a parallelogram, the measure of ∠ JML is equal to the measure of ∠ JKL by the Parallelogram Opposite Angles Theorem.

Next, by the Parallelogram Consecutive Angles Theorem we can see that ∠ KJM and ∠ JKL are supplementary, so the sum of their measures is 180^(∘). m∠ KJM+m∠ JKL=180^(∘) ⇓ m∠ KJM+ 60^(∘)=180^(∘) ⇓ m∠ KJM= 120^(∘) The measure of ∠ KJM is 120^(∘). Notice that since ∠ KJM and ∠ KLM are opposite angles they will have the same measure.

c In this part we are given that LM∥NO and NO∥PQ. The theorem that tells us about more than one pair of parallel lines is the Transitive Property of Parallel Lines. Let's recall it!

Transitive Property of Parallel Lines
If two lines are parallel to the same line, then they are parallel to each other.

Since JK and LM are opposite sides of a parallelogram they are parallel. This means that JK and NO are parallel by the Transitive Property of Parallel Lines. JK∥LMandLM∥NO ⇓ JK∥NO Next, since we are given that NO and PQ are parallel we can see that by the same theorem JK also needs to be parallel to PQ. JK∥NOandNO∥PQ ⇓ JK∥PQ

Subchapter links

Communicate Your Answer p.375

Monitoring Progress p.377-380

Exercises p.381-384

Exercise 34 Page 383

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