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
The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses.
The Distributive Property tells us that we can remove the parentheses if the term that the polynomial is being multiplied by is distributed to, or multiplied with each term inside the parentheses.
If a number outside the parentheses has a negative sign then the first and simplest way is to change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs. Similarly, positive or plus signs become negative or minus signs.
Answer:
yes yes yes yes no yes hcycrztdugguib
Answer: the equivalent equation is found by distributing the 1/4 to get 4+3x=28
the first step is subtract 4 to both sides
the second step is divide both sides by 3
the answer is x=8
Step-by-step explanation: