The base angles of an isosceles trapezoid are equal. Therefore:
20x + 9 = 14x + 15
6x = 6
x = 1
So, the base angles both equal 29 degrees.
In a trapezoid, the sum of the angles attached to the same leg always = 180 degrees.
Therefore, angle K and angle L equal 151 degrees.
Answer:
yes at an average of 150 pizzas a day they both sell about the same by the end of the week
I think that first you need to understand what CPCTC is used for.
Let's start with the definition of congruent triangles.
Definition of congruent triangles
Two triangles are congruent if each side of one triangle is congruent to a corresponding side of the other triangle and each angle of one triangle is congruent to a corresponding angle of the other triangle.
A definition works two ways.
1) If you are told the sides and angles of one triangle are congruent to the corresponding sides and angle of a second triangle, then you can conclude the triangles are congruent.
2) If you are told the triangles are congruent, then you can conclude 6 statements of congruence, 3 for sides and 3 for angles.
Now let's see what CPCTC is and how it works.
CPCTC stands for "corresponding parts of congruent triangles are congruent."
The way it works is this. You can prove triangles congruent by knowing fewer that 6 statements of congruence. You can use ASA, SAS, AAS, SSS, etc. Once you prove two triangles congruent, then by the definition of congruent triangles, there are 6 congruent statements. That is where CPCTC comes in. Once you prove the triangles congruent, then you can conclude two corresponding sides or two corresponding angles are congruent by CPCTC. These two corresponding parts were not involved in proving the triangles congruent.
Problem 1.
Statements Reasons
1. Seg. AD perp. seg. BC 1. Given
2. <ADB & <ADC are right angles 2. Def. of perp. lines
3. <ADB is congr. <ADC 3. All right angles are congruent
4. Seg. BD is congr. seg CD 4. Given
5. Seg. AD is congr. seg. AD 5. Congruence of segments is reflexive
6. Tr. ABD is congr. tr. ACD 6. SAS
7. Seg. AB is congr. seg. AC 7. CPCTC
Answer:
The area of the triangle on left is 9
in², the area of the triangle on the right is 9
in², and the area of the rectangle is 108
in².
The area of the trapezoid is the sum of these areas, which is 126
in².
Your answer is A: 15 inches by 15√3 inches.
We can use trigonometry to solve this. If we draw out one of the triangles we can label the 30 inch side as the hypotenuse, and then the other sides as the opposite and adjacent. Then we just have to find the lengths of these.
To find the opposite, we use the trigonometric ratio sinθ = opposite ÷ hypotenuse, and thus the opposite is sin(60) × 30 = 15√3
Automatically now we know the answer is A because that is the only option with 15√3 as a side, but you could also solve using cosθ = adjacent ÷ hypotenuse and get the other side.
I hope this helps!