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Core Connections Integrated II, 2015

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Core Connections Integrated II, 2015 View details

2. Section 7.2

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Exercise 115 Page 416

Consider the HL (Hypotenuse Leg) Congruence Theorem.

Congruent? Yes.
Flowchart: See solution.
x=32

Practice makes perfect

Let's label the vertices of the given triangles.

From the diagram we see that the triangles are right triangles. If we can prove that a pair of legs and the hypotenuses are congruent, we can use the HL (Hypotenuse Leg) Congruence Theorem to prove congruence. By using the Pythagorean Theorem, we can calculate the unknown leg or hypotenuse in either of the triangles.

a^2+b^2=c^2

a= 9, b= 40

9+ 40^2=c^2

▼

Solve for c

Calculate power

81+1600=c^2

Add terms

1681=c^2

Rearrange equation

c^2=1681

sqrt(LHS)=sqrt(RHS)

c=± 41

c > 0

c=41

As we can see, the two triangles have congruent hypotenuses and a pair of congruent legs. Therefore, they are congruent according to the HL Congruence Theorem. Let's show this as a flowchart.

Now, let's find x. Consider the diagram again.

Examining the diagram, we see that x spans part of the hypotenuse in one of the triangles. Since the second part of the hypotenuse coincides with the shorter leg of the other triangle (which must be 9) we can write and solve an equation for x. x+ 9=41 ⇔ x=32

Subchapter links

7.2.1 Conditional Probability and Independence p.401-402

7.2.2 More Conditional Probability p.406-409

7.2.3 Applications of Probability p.415-417