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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 6.2

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Exercise 89 Page 353

Examining the diagram, what information can you conclude about the triangles?

E.

Practice makes perfect

To prove congruence between two triangles, we need to know at least one of the following:

Three pairs of congruent sides.
Two pairs of sides and the included angle are congruent.
At least two pairs of congruent angles and one pair of congruent corresponding sides.

Of the four options, A-D, only three of them are viable theorems for claiming congruence.

B.& HL ≅ C.& SAS ≅ D.& SSS ≅ Of these three, B requires right triangles. From the diagram, we see that there are no indication of the triangles being right triangles, and therefore to claim congruence we have to use either SAS ≅ or SSS ≅.

What Do We Know From the Diagram?

Examining the diagram, we can identify a pair of alternate interior angles. Because the two lines cut by the third line are parallel, we know they are congruent according to the Alternate Interior Angles Theorem.

We also see that the triangles share a side. Therefore, we know that this side is congruent by the Reflexive Property of Congruence.

We can claim congruence by the AAS (Angle-Angle-Side) Congruence Theorem. However, this is not represented in either of the options. Therefore, the correct option is E.

Subchapter links

6.2.1 At Your Service p.340

6.2.2 Angles on a Pool Table p.343-344

6.2.3 Shortest Distance Problems p.347-348

6.2.4 The Number System and Deriving the Quadratic Formula p.353

6.2.5 The Number System and Deriving the Quadratic Formula p.355-356

6.2.6 Analyzing a Game p.359-360