08.03.2021

Can a rectangle be drawn with two opposite angles equal to 105°.

. 4

Faq

Mathematics
Step-by-step answer
P Answered by PhD

Look at the shaded areas and then read A. A rectangle has 2 sets of parallel lines (as these two figures do) and 1 right angle somewhere.  These two shaded regions do not have 1 right angle.

B: B is not correct because the shaded figures have 2 sets of 2 equal lines. A rhombus has 4 equal lines.

C: Not true either. The lines have 2 sets of parallel lines. Trapezoids have only 1 set.

D.  D is true

E.  E is true.


Perhaps you are not supposed to consider what the figures look like. I don't know how to answer the question. You likely got the same answers I did. Any chance you copied the wrong diagram?

Mathematics
Step-by-step answer
P Answered by Specialist

Area of shaded triangle = one - half times 24 square units.

Step-by-step explanation:

The line that is drawn from one corner to the opposite corner is called the diagonal of the rectangle.

The diagonal splits the rectangle into 2 right angled triangle of same measurements.

Therefore,

Area \ of\ rectangle\  =\  Area \ of \ triangle + Area  \ of \ triangle \\\\Area \ of\ rectangle\  =\  2 \times\  Area \ of \ triangle\\\\24 = 2 \times Area \ of \ triangle\\\\Area \ of \ triangle = \frac{1}{2} \times 24

Mathematics
Step-by-step answer
P Answered by PhD

Look at the shaded areas and then read A. A rectangle has 2 sets of parallel lines (as these two figures do) and 1 right angle somewhere.  These two shaded regions do not have 1 right angle.

B: B is not correct because the shaded figures have 2 sets of 2 equal lines. A rhombus has 4 equal lines.

C: Not true either. The lines have 2 sets of parallel lines. Trapezoids have only 1 set.

D.  D is true

E.  E is true.


Perhaps you are not supposed to consider what the figures look like. I don't know how to answer the question. You likely got the same answers I did. Any chance you copied the wrong diagram?

Mathematics
Step-by-step answer
P Answered by PhD

We have to prove that rectangles are parallelograms with congruent Diagonals.

Solution:

1. ∠R=∠E=∠C=∠T=90°

2. ER= CT, EC ║RT

3.  Diagonals E T and C R are drawn.

4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]

5.  Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]

6. In Δ ERT and Δ CTR

(a) ER= CT→→[Opposite sides of parallelogram]

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

(c) Side TR is Common.

So, Δ ERT ≅ Δ CTR→→[SAS]

Diagonal ET= Diagonal CR →→→[CPCTC]

In step 6, while proving Δ E RT ≅ Δ CTR, we have used

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.


Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruen
Mathematics
Step-by-step answer
P Answered by PhD

We have to prove that rectangles are parallelograms with congruent Diagonals.

Solution:

1. ∠R=∠E=∠C=∠T=90°

2. ER= CT, EC ║RT

3.  Diagonals E T and C R are drawn.

4. Shows Quadrilateral R E CT is a Rectangle.→→[Because if in a Quadrilateral One pair of Opposite sides are equal and parallel and each of the interior angle is right angle than it is a Rectangle.]

5.  Quadrilateral RECT is a Parallelogram.→→[If in a Quadrilateral one pair of opposite sides are equal and parallel then it is a Parallelogram]

6. In Δ ERT and Δ CTR

(a) ER= CT→→[Opposite sides of parallelogram]

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

(c) Side TR is Common.

So, Δ ERT ≅ Δ CTR→→[SAS]

Diagonal ET= Diagonal CR →→→[CPCTC]

In step 6, while proving Δ E RT ≅ Δ CTR, we have used

(b) ∠R + ∠T= 90° + 90°=180°→→→Because RECT is a rectangle, so ∠R=∠T=90°]

Here we have used ,Option (D) : Same-Side Interior Angles Theorem, which states that Sum of interior angles on same side of Transversal is supplementary.


Spencer wrote the following paragraph proof showing that rectangles are parallelograms with congruen
Mathematics
Step-by-step answer
P Answered by PhD

B. The two triangles are congruent but are oriented differently.


Step-by-step explanation:

Let ABCD is a rectangle and we draw a line to join vertex A and C such that the  line divides each of the right angles into two angles of measures 32° and 58° as in the figure

then in ΔABC and ΔCDA

AB=CD and AD=BC [opposite sides of rectangle are equal]

AC=AC [ reflexive property]

⇒ ΔABC ≅ ΔCDA [SSS congruence criteria]

Thus triangles are congruent but are oriented differently (from the picture)


Linnea has drawn a line from one corner of a rectangle to the opposite corner. the line divides each
Mathematics
Step-by-step answer
P Answered by PhD

Both are Scalene right angle triangle  90 °, 58 ° 32°

We know the length of the first triangle has different lengths, just like the other triangle is the same and this has different lengths. This is why we call them scalene right angles, as they both have 90 ° on the corners that went untouched within the rectangle.

Step-by-step explanation:

Lena has drawn a line from one corner of a rectangle to the opposite corner. The lines dividing each of the right angles, being two angles, each measure 32 and 58 which David best describes the resulting triangles.

If two angles are opposite ends one is 32 degree, the other is 58-

Then either triangles for two angles total 90 each and therefore being a rectangle show the rectangle had regular 90 degree corners before being divided. We cna check this as after lines being drawn corner end to its corner opposite we see each have a supplementary angle of 32 or 58 = 90 and 90 should we draw a line from the corner exterior to make a straight line appear longer on each base or its parallel base or top on the opposite corner. As long as they are drawn parallel exterior corner lines and where 90 degree is highlighted looking like L's on each too.

if the triangles are 32 + 58 either end then their 3rd angle on each triangle will be 90 where we call this triangle simply scalene right angle triangle as no sides are the same length within the triangle.

Mathematics
Step-by-step answer
P Answered by PhD

Both are Scalene right angle triangle  90 °, 58 ° 32°

We know the length of the first triangle has different lengths, just like the other triangle is the same and this has different lengths. This is why we call them scalene right angles, as they both have 90 ° on the corners that went untouched within the rectangle.

Step-by-step explanation:

Lena has drawn a line from one corner of a rectangle to the opposite corner. The lines dividing each of the right angles, being two angles, each measure 32 and 58 which David best describes the resulting triangles.

If two angles are opposite ends one is 32 degree, the other is 58-

Then either triangles for two angles total 90 each and therefore being a rectangle show the rectangle had regular 90 degree corners before being divided. We cna check this as after lines being drawn corner end to its corner opposite we see each have a supplementary angle of 32 or 58 = 90 and 90 should we draw a line from the corner exterior to make a straight line appear longer on each base or its parallel base or top on the opposite corner. As long as they are drawn parallel exterior corner lines and where 90 degree is highlighted looking like L's on each too.

if the triangles are 32 + 58 either end then their 3rd angle on each triangle will be 90 where we call this triangle simply scalene right angle triangle as no sides are the same length within the triangle.

Try asking the Studen AI a question.

It will provide an instant answer!

FREE