body{margin:0;} noscript{z-index: 10000; position: fixed; display: block; height: 100%; width: 100%; background: #fff;} noscript .fa{font-size: 40px; display:block; color: #daa520;} noscript div{margin-top: 6%; padding-left: 20px; padding-right: 20px; text-align: center;} ! You must have JavaScript enabled to use this site.

Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

6. Describing Pairs of Angles

Continue to next subchapter

Exercise 48 Page 430

Begin by creating a diagram of the situation. What do you know about each angle?

Yes, the classmate is correct. See solution.

Practice makes perfect

Let's begin by creating a diagram showing the angles we are going to examine in this exercise.

We can assume that the ∠ QPU is straight since it represents a mirror. Therefore we can calculate m∠ QPS using the Angle Addition Postulate.

∠ QPS + ∠ UPS = ∠ QPU

∠ UPS= 90^(∘), ∠ QPU= 180^(∘)

∠ QPS + 90^(∘) = 180^(∘)

LHS-90^(∘)=RHS-90^(∘)

∠ QPS = 180^(∘) - 90^(∘)

Subtract term

∠ QPS = 90^(∘)

We now know that ∠ QPS is a right angle. Let's mark this in the diagram.

Now we know that there are two sets of complementary angles. m∠ QPR+m∠ RPS=90^(∘) m∠ SPT+m∠ TPU=90^(∘) Using substitution, we can form an equation. From there, we can use substitution again to see if ∠ QPR ≅ ∠ TPU.

m∠ QPR+m∠ RPS = m∠ SPT+m∠ TPU

m∠ SPT= m∠ RPS

m∠ QPR+m∠ RPS = m∠ RPS+m∠ TPU

LHS-m∠ RPS=RHS-m∠ RPS

m∠ QPR = m∠ TPU

We have shown m∠ QPR = m∠ TPU, which means that these angles are always congruent. This means our classmate is correct.

Subchapter links

Communicate Your Answer p.423

Monitoring Progress p.425-427

Exercises p.428-430