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raketka [301]
3 years ago
8

Prove the Converse of the Pythagorean Theorem using similar triangles. The Converse of the Pythagorean Theorem states that when

the sum of the squares of the lengths of the legs of the triangle equals the squared length of the hypotenuse, the triangle is a right triangle. Be sure to create and name the appropriate geometric figures. (10 points)
Let ACB be a triangle where segment AB is labeled c, segment BC is labeled a, and segment CA is labeled b. Using a compass and straightedge, construct right triangle XZY with legs XZ and ZY congruent to legs AC and CB , respectively. Let XZ be labeled y, ZY labeled x, and YX labeled z. Therefore, y = b and x = a. Because triangle XZY was constructed as a right triangle, x^2 + y^2 = z^2 by the _____ _____. By _____, a^2 + b^2 = z^2. According to the given information, a^2 + b^2 = c^2. By the _____ _____ _____ _____, c^2 = z^2. Use the _____ _____ _____ _____ _____ to take the square root of both sides of the equation to result in the equation c = z. By the ______ _____, triangles ACB and XZY are congruent. Consequently, by _____, triangle ACB is a right triangle.


2. Look at the figure below:




Copy the Statements and Reasons into your answer box.

Statements
Reasons
Angle PQS in triangle PQS is congruent to angle PRQ in triangle PRQ


Angle QPS is common to both triangle PRQ and triangle PQS


Triangle PRQ is similar to triangle PQS




Look at the figure.





3. Annie walks 15 feet away from her house and places a mirror on the ground. She backs 4 feet away from the mirror so that she can see the tip of the roof. Annie’s eyes are 5 feet above the ground. Annie and the house are both perpendicular to the ground. The angles between the top of the house, the mirror, and the ground and between Annie’s eyes, the mirror, and the ground are congruent as shown in the image:




What is the height of the house? Show your work and explain your reasoning in complete sentences.

The triangle formed by the person, the mirror, and the ground is similar to the triangle formed by the house, the mirror, and the ground. The distance between the mirror and the person is 4 feet. The distance between the mirror and the house is 15 feet. The distance between the ground and the person’s eye level is 5 feet. Let x = the height of the house.
Mathematics
1 answer:
Virty [35]3 years ago
4 0

Answer:

EF = BC = a ÐF is a right angle. FD = CA = b triangle EF = BC = a angle F is a right angle. FD = CA = b In triangle DEF, By Pythagoras Theorem, a2 + b2 = c2 the given AB=c= a^2 + b^2 square root Theorefore AB = DE But by construction, BC = EF and CA = FD triangle ABC congruent to DEF (S.S.S

We have given that Δ ABC is similar to Δ CBD and Δ ABC is similar to Δ ACD according to the attached picture.

Because of the similarity the corresponding sides are proportional. Then a/c = f/a

and b/e = c/b. If we cross multiply, we'll get

a² = cf and b² = ce

If we add these equalities together, we'll get

a² + b² = c (f + e)

From the beginning, we know that c = e+f

Then, the final result is:

a² + b² = c²

You might be interested in
A=1/2 (a+b)h work out A if a=2 b=7 h=3
BartSMP [9]

Step-by-step explanation:

A =1/2(a+b)h

  • 1/2(2+7)3
  • 1/2×27
  • 13.5

hope it helps.

6 0
2 years ago
What is the graph for {3x+5y<10 {x-y<=1
Nostrana [21]
Sounds to me as tho you are to graph 3x+5y<10, and that after doing so you are to restrict the shaded answer area created by the "constraint" inequality x≤y+1.    OR x-1 ≤ y   OR  y≥x-1.  If this is the correct assumption, then please finish the last part of y our problem statement by typing   {x-y<=1}.

First graph 3x+5y = 10, using a dashed line instead of a solid line.

x-intercept will be 10/3 and y-intercept will be 2.  Now, because of the < symbol, shade the coordinate plane BELOW this dashed line.

Next, graph y=x-1.  y-intercept is -1 and x intercept is 1.  Shade the graph area ABOVE this solid line.

The 2 lines intersect at (1.875, 0.875).  To the LEFT of this point is a wedge-shaped area bounded by the 2 lines mentioned.  That wedge-shaped area is the solution set for this problem.
6 0
3 years ago
Use dimensional analysis to convert the quantity to the indicated units.
Eva8 [605]

Answer:

27 ft = 324 inches

Step-by-step explanation:

We want to use dimensional analysis to convert a quantity here

27 ft to inches

Mathematically;

12 inches = 1 ft

so;

x inches = 27 ft

So the number of inches will be 27 * 12 = 324 inches

4 0
3 years ago
A salesperson receives a weekly salary of ​$400400. In​ addition, ​$3030 is paid for every item sold in excess of 200200 items.
Elanso [62]
I think you have to multiply them. If you have a calculator you can do it easily.

3 0
3 years ago
Help as soon as possible!
Vika [28.1K]

Answer:

(7 + x + a)(7 - x - a)

Here you buddy hope it helps!

6 0
2 years ago
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