1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
raketka [301]
3 years ago
15

If ABCD is an A4 sheet and BCPO is the square, prove that △OCD is an isosceles triangle. And find the angles marked as 1 to 8 wi

thout using a protractor
Mathematics
1 answer:
Dmitry [639]3 years ago
3 0

Answer:

The diagram for the question is missing, but I found an appropriate diagram fo the question:

Proof:

since OC = CD = 297mm Therefore, Δ OCD is an isoscless triangle

∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

∠DOP = 22.5°

∠PDO = 67.5°

∠ADO = 22.5°

∠AOD = 67.5°

Step-by-step explanation:

Given:

AB = CD = 297 mm

AD = BC = 210 mm

BCPO is a square

∴ BC = OP = CP = OB = 210mm

Solving for OC

OCB is a right anlgled triangle

using Pythagoras theorem

(Hypotenuse)² = Sum of square of the other two sides

(OC)² = (OB)² + (BC)²

(OC)² = 210² + 210²

(OC)² = 44100 + 44100

OC = √(88200

OC = 296.98 = 297

OC = 297mm

An isosceless tringle is a triangle that has two equal sides

Therefore for △OCD

CD = OC = 297mm; Hence, △OCD is an isosceless triangle.

The marked angles are not given in the diagram, but I am assuming it is all the angles other than the 90° angles

Since BC = OB = 210mm

∠BCO = ∠BOC

since sum of angles in a triangle = 180°

∠BCO + ∠BOC + 90 = 180

(∠BCO + ∠BOC) = 180 - 90

(∠BCO + ∠BOC) = 90°

since ∠BCO = ∠BOC

∴  ∠BCO = ∠BOC = 90/2 = 45

∴ ∠BCO = 45°

∠BOC = 45°

∠PCO = 45°

∠POC = 45°

For ΔOPD

Tan\ \theta = \frac{opposite}{adjacent}\\ Tan\ (\angle DOP) = \frac{87}{210} \\(\angle DOP) = Tan^-1(0.414)\\(\angle DOP) = 22.5 ^{\circ}

Note that DP = 297 - 210 = 87mm

∠PDO + ∠DOP + 90 = 180

∠PDO + 22.5 + 90 = 180

∠PDO = 180 - 90 - 22.5

∠PDO = 67.5°

∠ADO = 22.5° (alternate to ∠DOP)

∠AOD = 67.5° (Alternate to ∠PDO)

You might be interested in
NEED ANSWER ASAP!!! PLEASE HELP
lys-0071 [83]

Answer:

Answer "C"

Step-by-step explanation:

I believe this because it would not make sense to compare the already known equation to the unknown equation and does make sense to compare the unknown equation to the known equation

(pls dont delete this moderators)

3 0
3 years ago
How to solve step by step
jasenka [17]
X² = 16

the way to isolate your x variable is to square root both sides

√x² = √16
x = <span>± 4

so your answers are 4 and -4</span>
3 0
3 years ago
The sum of a number times 6 and 4 equals 5
Inessa [10]
5= (6+4)x
5= 10x

5= 10x           then divide by 10 to get the variable by itself      
__ ___
10   10
.5 = x                               you can use .5 or 1/2


hope this helps!
:)

3 0
3 years ago
Just # 16<br><br>idk what it's "counting" by
zysi [14]
For #16, every input by +1 has an output of +7.

9 + 7 = 16
16 + 7 = 23
23 + 7 = 30.....
3 0
3 years ago
Due in 10!!! Fill in the blanks…
Alenkinab [10]

sorry this is late!!

#1 - A circular grid like this one can be helpful for performing dilations

#2 - To perform a dilation, we need a (In order to perform a dilation, students will need to know the center of dilation (which can be communicated using the coordinate grid), the coordinates of the polygon that they are dilating (also communicated using the coordinate grid), and the scale factor.)

5 0
3 years ago
Other questions:
  • A square has a side length of 22 meters what is the area of the square
    7·1 answer
  • The product of 16 and x is equal to 32
    13·1 answer
  • What is the y-intercept of f–1(x)?
    13·1 answer
  • the legs of a right triangle are 18 cm and 80 cm. what is the length of the hypotenuse? 82 cm 85 cm 89 cm 98 cm
    7·2 answers
  • Sabrina is ordering a custom circular glass table for her dining room. The tables are ordered based on the area of the tabletop,
    9·1 answer
  • Carly is a catcher on the school softball team. By the end of the season she played 45% of the 40 games the team played. In how
    5·2 answers
  • 1) Television sizes are a measurement of the length of a TV's diagonal. If a 65-inch TV has
    9·1 answer
  • Can someone help me answer this question plz and thank you
    15·2 answers
  • Twice the difference of x and 6 is greater than the reciprocal of 2.
    8·1 answer
  • Use the discriminant to determine the type and number of solutions.
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!