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Core Connections Integrated II, 2015 View details

1. Section 7.1

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Exercise 9 Page 376

Consider the Reflexive Property of Congruence.

Congruent? Yes.
x=2
Flowchart: See solution.

Practice makes perfect

Examining the diagram, we notice that the triangles have a pair of congruent sides and a pair of congruent angles. Additionally, the two triangles share a side. According to the Reflexive Property of Congruence, this side must be congruent as well. Let's add this to the diagram and label the vertices.

Since two pairs of sides and their included angle are congruent, by the SAS (Side-Angle-Side) Congruence Theorem we can claim that the triangles are congruent. Let's show this as a flowchart.

To find the value of x, remember that AB and CD are corresponding congruent sides. Since we have been given expressions containing x for both of these sides, we can equate them and solve for x.

8x+2=6x+6

SubEqn

LHS-2=RHS-2

8x=6x+4

SubEqn

LHS-6x=RHS-6x

2x=4

DivEqn

.LHS /2.=.RHS /2.

x=2