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:
Angle 1 is 62°
Angle 2 is 45°
Angle 3 is 24°
Step-by-step explanation:
Answer:
x-y=-2
Step-by-step explanation:
Divide both sides if the equations by 3.
(3y-3x)÷3=6÷3
y-3x÷3=2
calculate the quotient
y-x=2
multiply both sides of the equation bub -1
-1x(-x)-1y=-1x2
any expression multiplied by -1
x-1y=-1x2
any expression multiplied by 1 remains the same.
x--y=-1x2
x-y=-2
You have a 1/2 chance of spinning an even number on the spinner, and a 1/2 chance of rolling an odd number on the die, 1/2 times 1/2 give you a 1/4 chance of doing both of those tasks.
Answer:
5.29
Step-by-step explanation:
Pythagorean theorem is used
We will call AB x
x^2 + 6^2 = 8^2
x^2 + 36 = 64
x^2 = 28
x = 5.2915026
<u>x = 5.26</u>