Question

Given:
Square with side c.
All four interior triangles are right triangles.
All four interior triangles are congruent.
The interior quadrilateral is a square.

Prove:
a2 + b2 = c2

Answer 1

When written in the correct order, the paragraph below proves the Pythagorean Theorem using the diagram.

Let a represent the height and b represent the base of each triangle.

The area of one triangle is represented by the expression ab.

The area of all four triangles will be represented by 4 • ab or 2ab.

(1) The area of the exterior square is found by squaring side c, which is c2, or by adding the areas of the four interior triangles and interior square, 2ab + a2 – 2ab + b2.

(2) By distribution, the area is a2 – 2ab + b2.

(3) The length of a side of the interior square is (a – b).

(4) The area of the interior square is (a – b)2.

Therefore, c2 = 2ab + a2 – 2ab + b2.

Through addition, c2 = a2 + b2.

Answer Choices:

Which is the most logical order of statements (1), (2), (3), and (4) to complete the proof?

(3), (4), (2), (1) ----> This is the answer I chose

(3), (1), (4), (2)

(3), (1), (2), (4)

(3), (4), (1), (2)

Answer 2

@ganeshie8 - Is the answer I chose correct?

Answer 3

Yes. thats the correct one, good work !

Answer 4

I have a few more, if you can check them and make sure I got the right answer? @ganeshie8

Answer 5

sure post them il see if i can help :)

Answer 6

Given: ∆BCA is a right triangle.
Prove: a2 + b2 = c2

The two-column proof with missing justifications proves the Pythagorean Theorem using similar triangles.

Answer Choices:

Which is NOT a justification for the proof?
Addition Property of Equality

Pythagorean Theorem ---> this is the answer I chose

Pieces of Right Triangles Similarity Theorem

Cross Product Property

Answer 7

Given: In ∆ABC below, BD/BA = BE/BC
Prove: segment DE || segment AC

The flow chart proof with missing statements and reasons proves that if a line intersects two sides of a triangle and divides these sides proportionally, the line is parallel to the third side.

Which statement and reason can be used to fill in the numbered blank spaces?

1. ∡A ≅ ∡B
2. Corresponding Parts of Similar Triangles

1. ∡A ≅ ∡B
2. Corresponding Angles Postulate

1. ∡B ≅ ∡B
2. Reflexive Property of Equality ---> this is my answer

1. ∡A ≅ ∡A
2. Reflexive Property of Equality

Answer 8

Here is the triangle attachment for ^^

Answer 9

This is the last one -

Given: In ∆ACB, c2 = a2 + b2.
Prove: ∆ACB is a right angle.

Complete the flow chart proof with missing reasons to prove that ∆ACB is a right angle.

Which pair of reasons correctly completes this proof?

Reason #1 - Reflexive Property of Equality
Reason #2 - SSS Postulate

Reason #1 - Substitution
Reason #2 - SAS Postulate

Reason #1 - Substitution
Reason #2 - SSS Postulate ----> This is my answer

Reason #1 - Reflexive Property of Equality
Reason #2 - SAS Postulate

Answer 10

first two are correct. let me check the last one..

Answer 11

Okay! (:

Answer 12

All correct ! wonderful work !!!

Answer 13

Awesome! Thank you! I have two questions, that I'm having trouble figuring out.

Here is the first one:

Which statement corrects the flaw in Gina's proof?

The coordinates of D and E were found using the Midpoint Formula.

Segments DE and AC are parallel by construction.

The slope of segments DE and AC is not 0.

The coordinates of D and E were found using the Distance between Two Points Postulate

Answer 14

slope formula cannot give coordinates of midpoints of sides.

so, the answer would be this :-

The coordinates of D and E were found using the Midpoint Formula.

Answer 15

Thank you! Here is the last question:

Given: ∆ABC

Prove: The three medians of ∆ABC intersect at a common point.

When written in the correct order, the two-column proof below describes the statements and justifications for proving the three medians of a triangle all intersect in one point.

Which is the most logical order of statements and justifications I, II, III, and IV to complete the proof?

II, III, I, IV

III, II, I, IV

II, III, IV, I

III, II, IV, I

Answer 16

@ganeshie8

Answer 17

look at this order:-

II, III, IV, I

Answer 18

So, Midsegment Theorem, Substitution, Properties of a Parallelogram (opposite sides are parallel), and then Properties of a Parallelogram (diagonals bisect each other) ?

Answer 19

thats it !

Answer 20

Thank you!

Answer 21

you're wc :)