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Seth is using the figure shown below to prove Pythagorean Theorem using triangle similarly In the given triangle ABC, angle A ls 90 and segment AD is perpendicular to segment BC Part A: Identify a pair of similar triangles (2 points) Part B: Explain how you know the triangles from Part A are similar (4 points) Part C: I DB = 9 and DC = 4, find the length of segment DA Show your work (4 points)

Seth Is Using The Figure Shown Below To Prove Pythagorean Theorem Using Triangle Similarly In The Given Triangle ABC Angle A Ls 90 And Segment AD Is Perpendicul class=

Sagot :

a)

The pair of similar triangles are triangles ABD and ACD

b)

The triangle is given such that angle A is 90°

If point D is on line BC, then it touches angle A. However line AD is perpendicular to line BC,which means it splits the angle at A into two equal halves.

Hence, you now have two right angled triangles, on the one hand, triangle ABD and on the other hand, triangle ACD. The first one has angle D measuring 90° and line AB as the hypotenuse. The second one also has angle D measuring 90° with it's hypotenuse at line AC.

c)

The angle A which is 90 degree has been splitted into two(2) equal halves by the line segment AD, thus each angle is 45 degrees.

This is shown in the diagram below:

Applying the Tangent trigonometry ratio to solve for the line segment DA, we have:

[tex]\begin{gathered} \text{Tan 45}^0=\frac{opposite}{adjacent} \\ \text{Tan 45=}\frac{9}{|DA|} \\ 1=\frac{9}{|DA|} \\ |DA|=9 \end{gathered}[/tex]

Hence, the length of the line segment DA is 9 units

View image TanveerP779066
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