Question

I really need help! I have 5 questions! I will give medals!

Answer 1

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

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

Which is NOT a justification for the proof?

Addition Property of Equality

Pythagorean Theorem

Pieces of Right Triangles Similarity Theorem

Cross Product Property

Answer 2

Given: In ∆ABC below,BD over BA equals BE over BC .
Prove: segment DE is parallel to segment AC
Triangles ABC and DBE where BD is to BA as BE is to BC.

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. ∡BDE ≅ ∡BAC
2. Corresponding Parts of Similar Triangles

1. ∡BDE ≅ ∡BCA
2. Alternate Exterior Theorem

1. ∡BDE ≅ ∡BAC
2. Corresponding Angles Postulate

1. ∡BDE ≅ ∡BCA
2. Corresponding Parts of Similar Triangles

Answer 3

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

Square with side length c; four right triangles with hypotenuse with length c and legs measuring a and b; the interior quadrilateral is a square.

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 One halfab.

The area of all four triangles will be represented by 4 • One halfab 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.

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

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

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

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

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

Answer 4

Triangles ACB and DFE are shown below.

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 - Pythagorean Theorem
Reason #2 - Transitive Property of Equality

Reason #1 - Definition of a Right Triangle
Reason #2 - Reflexive Property of Equality

Reason #1 - Pythagorean Theorem
Reason #2 - Reflexive Property of Equality

Reason #1 - Definition of a Right Triangle
Reason #2 - Transitive Property of Equality

Answer 5

Given: In ∆ABC, segment DE is parallel to segment AC .
Prove: BD over BA equals BE over BC

Triangles ABC and DBE where DE is parallel to AC.

The two-column proof with missing statements and reasons proves that if a line parallel to one side of a triangle also intersects the other two sides, the line divides the sides proportionally.

Complete the proof by entering the correct statements and reasons.

Answer 6

@andriod09?
@ajprincess?
@BABYShawol184?
@TheDarkKnight?

can someone help?