Exercise 123 Page 269

a Similar triangles have three congruent corresponding angles. We already know that one pair of angles in the triangles are congruent. Since, we also know the measure of a second angle in both triangles, we can determine the third angle's measure by using the Triangle Angle Sum Theorem.

62^(∘)+32^(∘)+m∠ ABC = 180^(∘) 82^(∘)+32^(∘)+m∠ EFD = 180^(∘) Let's solve for m∠ ABC in the first equation.

62+32+m∠ ABC = 180

AddTerms

Add terms

94+m∠ ABC = 180

SubEqn

LHS-94^(∘)=RHS-94^(∘)

m∠ ABC = 86

Since both triangles have an angle that is 86^(∘), we know that two pairs of angles are congruent. With this information, we do not have to solve for m∠ EFD since we can already claim similarity by the Angle Angle Simililarity Theorem. Let's write this as a flowchart.

In similar shapes, the ratio between any pair of corresponding sides is always equal. Let's identify corresponding sides in the two triangles.

Let's solve for x in the equation from the diagram.

x/2.4=6/4

▼

Solve for x

ReduceFrac

a/b=.a /2./.b /2.

x/2.4=3/2

MultEqn

LHS * 2.4=RHS* 2.4

x=3/2* 2.4

MoveRightFacToNum

a/c* b = a* b/c

x=7.2/3

CalcQuot

Calculate quotient

x=3.6

b Notice that the triangles we are considering are △ BCD and △ ACE. From the diagram, we know that they have one pair of congruent corresponding angles. Additionally, we see that they share ∠ C as an angle.

Since, the triangles have two congruent corresponding angles, we can use the Angle-Angle Similarity Theorem and claim that they are similar. Let's show this as a flowchart.