Plz

what is the missing reason in steps 7 and 8 of the proof?

a. definition of cosine in right triangle

b. definition of sine in right triangle

c. definition of tangent in right triangle

d. corresponding sides of congruent triangles are equal

e. definition of equilateral triangle


Plz  what is the missing reason in steps 7 and 8 of the proof?  a. definitio

Answers

In ∆abd, bd = c sin a
definition of cosine in right triangle :   from a  triangle . given any angle q (0 £ q £ 90°), we can find the sine or  cosine   of that angle by constructing a  right triangle   with one vertex of angle q. the sine is equal to the length of the side opposite to q, divided by the length of the  triangle's   hypotenuse.

definition of sine in right triangle:   the  sine   function, along with cosine and tangent, is one of the three most common trigonometric functions. in any  right triangle , the  sine   of an angle x is the length of the opposite side (o) divided by the length of the hypotenuse (h)

definition of tangent in right triangle:   the  tangent   function, along with sine and cosine, is one of the three most common trigonometric functions. in any  right triangle , the  tangent   of an angle is the length of the opposite side (o) divided by the length of the adjacent side (a).

if three sides of one triangle are congruent to three sides of another triangle, the triangles are congruent

in geometry, an  equilateral triangle   is a  triangle   in which all three sides are equal. in the familiar euclidean geometry,equilateral triangles   are also equiangular; that is, all three internal angles are also congruent to each other and are each 60°.
Given the following statements and Reasons

1. WXYZ is a ▱; ZX ≅ WY 1. given
2. ZY ≅ WX 2. opp. sides of ▱ are ≅
3. YX ≅ YX 3. reflexive
4. △ZYX ≅ △WXY 4. SSS ≅ thm.
5. ∠ZYX ≅ ∠WXY 5. CPCTC
6. m∠ZYX ≅ m∠WXY 6. def. of ≅
7. m∠ZYX + m∠WXY = 180° 7. ?
8. m∠ZYX + m∠ZYX = 180° 8. substitution
9. 2(m∠ZYX) = 180° 9. simplification
10. m∠ZYX = 90° 10. div. prop. of equality
11. WXYZ is a rectangle 11. rectangle ∠ thm.

The missing reason in step 7 is "consecutive ∠s in a ▱ are supplementary"

the correct answer is:

definition of sine in right triangle

explanation:

the ratio for sine is opposite/hypotenuse. this means that for the sine of angle b, we want the side opposite b, which is ae, over the hypotenuse, which is c:

sin b = ae/c

multiply both sides by c:

c sin b = (ae/c)*c

c sin b = ae

this is by definition of sine.

this also applies to step 8.

Step-by-step explanation:

Given: WXYZ is a parallelogram, ZX ≅ WY

Prove: WXYZ is a rectangle

Proof:

Step 1. WXYZ is a parallelogram and ZX ≅ WY (Given)

Step 2. ZY ≅ WX (Opposite sides of parallelogram are congruent)

Step 3. YX ≅ YX  (Reflexive Property)

Step 4. Consider △ZYX and △WXY, we have

ZX ≅ WY (Given)

ZY ≅ WX (Opposite sides of parallelogram are congruent)

YX ≅ YX  (Reflexive Property)

Thus, by SSS rule, △ZYX ≅ △WXY

Step 5. By CPCTC, ∠ZYX ≅ ∠WXY

Step 6.  m∠ZYX ≅ m∠WXY (Definition of congruency)

Step 7.  m∠ZYX + m∠WXY = 180° ( consecutive ∠s in a parallelogram are supplementary)

Step 8. m∠ZYX + m∠ZYX = 180° (Substitution)

Step 9. 2(m∠ZYX) = 180° (Simplification)

Step 10.  m∠ZYX = 90°(Dividing property of equality)

Step 11. WXYZ is a rectangle (Rectangle angle theorem)

Hence proved.

Observe the given figure.

Given: WXYZ is a parallelogram and ZX \cong WY

To Prove: WXYZ is a rectangle

  Statements                                                                                      

1. WXYZ is a parallelogram and ZX \cong WY                

Reason: Given

2.  ZY \cong WX                                          

Reason: Opposite sides of parallelogram are equal.

3.  YX \cong YX

Reason: Reflexive

4.  \Delta ZYX \cong \Delta WXY

Reason: By SSS congruence theorem

5.  \angle ZYX \cong \angle WXY

Reason: CPCT

6.  m \angle ZYX \cong m \angle WXY

Reason: Def of congruency

7.  m \angle ZYX + m \angle WXY= 180^\circ

Reason: Consecutive angles in a parallelogram are supplementary.

"If a quadrilateral is a parallelogram, it has consecutive angles then they are supplementary".

8.  m \angle ZYX + m \angle ZYX= 180^\circ

Reason: Substitution.

9. 2(m \angle ZYX)= 180^\circ

Reason: Simplification

10. m \angle ZYX = 90^\circ

Reason: Division property of Equality

11. WXYZ is a rectangle

Reason: Rectangle angle theorem

D   took the quiz on edge   hope this helps!   :)

Step-by-step explanation:

Consider the diagram and proof below.

Given: WXYZ is a parallelogram, ZX ≅ WY

Prove: WXYZ is a rectangle

Parallelogram W X Y Z with diagonals is shown.

 

Statement

 

Reason

1.WXYZ is a ▱; ZX ≅ WY1.given

2.ZY ≅ WX2.opp. sides of ▱ are ≅

3.YX ≅ YX3.reflexive

4.△ZYX ≅ △WXY4.SSS ≅ thm.

5.∠ZYX ≅ ∠WXY5.CPCTC

6.m∠ZYX ≅ m∠WXY6.def. of ≅

7.m∠ZYX + m∠WXY = 180°7.?

8.m∠ZYX + m∠ZYX = 180°8.substitution

9.2(m∠ZYX) = 180°9.simplification

10.m∠ZYX = 90°10.div. prop. of equality

11.WXYZ is a rectangle11.rectangle ∠ thm.

What is the missing reason in Step 7?  

triangle angle sum theorem

quadrilateral angle sum theorem

definition of complementary

consecutive ∠s in a ▱ are supplementary

7's reason is consecutive angles of a parallelogram are supplementary.

Step-by-step explanation:

Hope this helps:)

  A. definition of sine in right triangle

Step-by-step explanation:

Steps 6 to 10 are a copy of steps 2 to 5, using different vertices and sides. Since the two developments are substantially identical, the reasons will be identical:

  reason 7 = reason 8 = reason 2 = reason 3 = "definition of sine in right triangle"

The missing reason in Step 7 is ' Consecutive interior angles add up to 180°'

Step-by-step explanation:

Since we know that, The sum of two consecutive interior angles made by same transversal on two parallel lines is always equal to 180°.

And, here ZY\parallel WX and XY is the common transversal, Also, ∠WYX and ∠WXY are the consecutive angles on lines ZY and WX respectively by transversal YX. ( shown on figure)

Therefore, m∠ZYX + m∠WXY = 180°

Here, Given, WXYZ is a parallelogram in which ZX\cong WY

we have to prove that: WXYZ is a rectangle.

            Statement                                              Reason

1. WXYZ is a parallelogram,                 1. Given

     ZX ≅WY

2.  ZY ≅ WX                                           2. opposite sides of parallelogram

                                                                  are congruent.

3.       YX≅YX                                        3. Reflexive

4.ΔZYX ≅ Δ WXY                             4.  SSS postulate of congruence

5.  ∠ZYX ≅ ∠WXY                                 5. CPCTC

6. m∠ZYX ≅ m∠WXY                            6. definition of congruence.

7.m∠ZYX + m∠WXY = 180°                   7.Consecutive interior                                                        

                                                                  angles add up to 180°'

8.m∠ZYX + m∠ZYX = 180°                    8. By substitution

9. 2(m∠ZYX) = 180°                                9. By simplification

10.m∠ZYX = 90°                                     10.division property of equality

11.WXYZ is a rectangle                       11.Rectangle angle theorem.



Consider the diagram and proof below. given:  wxyz is a parallelogram, zx ≅ wy prove:  wxyz is a rec

Option B. Definition of sine in right triangle.

Step-by-step explanation:

In step 7: ΔBAE, AE=c sinB

The answer is definition of sine in right triangle. Because, In a right angled triangle, the sine of an angle is equal to the length of the opposite side divided by hypotenuse.

By definition, \sin \theta=\frac{o p p}{h y p}

Thus, \begin{aligned}\sin B &=\frac{A E}{c} \\c \sin B &=A E\end{aligned}

Thus, the answer is definition of sine in right triangle.

In step 8: ΔCAE, AE=b sinC

The answer is definition of sine in right triangle. Because, In a right angled triangle, the sine of an angle is equal to the length of the opposite side divided by hypotenuse.

By definition, \sin \theta=\frac{o p p}{h y p}

Thus, \begin{array}{r}{\sin C=\frac{A E}{b}} \\{b \sin C=A E}\end{array}

Thus, the answer is definition of sine in right triangle.



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