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Big Ideas Math Integrated I, 2016

BI

Big Ideas Math Integrated I, 2016 View details

1. Translations

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Exercise 30 Page 549

Translations are congruence transformations. This means that they preserve side lengths and angle measures.

a=35
b=14
c=5

Practice makes perfect

Translations are congruence transformations. This means that they preserve side lengths and angle measures. Therefore, we can compare corresponding parts in both triangles to find the value of the variables. Let's start by paying close attention to the side lengths.

If two sides are congruent, then they have the same length. 4c-6=14 and b+6=20 Let's solve the above equations to find the values of b and c.

lc4c-6=14 & (I) b+6=20 & (II)

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Solve for b & c

(I): LHS+6=RHS+6

l4c=20 b+6=20

(I): .LHS /4.=.RHS /4.

lc=5 b+6=20

(II): LHS-6=RHS-6

lc=5 b=14

Let's deal with the angles now. Since the triangles are congruent, then corresponding angles are also congruent.

Therefore, in both triangles, since one of the angles is a right angle, the other two are complementary angles. a+55=90 ⇔ a=35

Subchapter links

Communicate Your Answer p.543

Monitoring Progress p.545-547

Exercises p.548-550