Geometry Homework Practice Workbook 1st Edition Chapter 2 Inductive Reasoning and Conjecture
Page 27 Problem 1 Answer
We have been given QA=QA in the question.
Here, we are asked to find the property of the given comparison.
Here, we have seen that both side parameter is same along with equal sign.
Therefore, we can say that it follows the reflexive property of equality which defines that a number or variable is equal to itself.
Hence, according to the given comparison QA=QA we have found that it follows the reflexive property of equality.
Page 27 Problem 2 Answer
We have been given AB≅BC, BC≅CE,AB≅CE in the question.
Here, we are asked to find the property among these comparisons.
Now, we have seen that all three sides are congruent to each other.
Finally, we will conclude that the given statement follows the transitive property of congruency which tells about similar shape and size.
Hence, using the given comparison AB≅BC,BC≅CE,AB≅CE we got that it followed the transitive property of congruency.
Page 27 Problem 3 Answer
We have been given PR=PQ+QR in the question.
We are asked to determine the property of the given comparison.
Here, we have seen that there are three points P,Q,R and Q is the midpoint.
Now, after evaluating the given comparison we can say that it follows the segment addition postulate which tells about the point on the line.
Hence, according to the given statement PR=PQ+QR we have found that it follows the segment addition postulate.
Page 27 Problem 4 Answer
We have been given AB+BC=EF+FG
AB+BC=AC
EF+FG=AC
Here, we are asked to find the property of the given statement in the question.
Now, we have seen that there is a comparison between the sum of two points with other one or two points.
Now, we can say that it follows substitution and transitive property which tells about replacing the values and similarity.
Hence, according to the given statements
AB+BC=EF+FG
AB+BC=AC
EF+FG=AC
We have got that this statement follows substitution and transitive property.
Page 27 Problem 5 Answer
We have been given two statements SU≅LR
TU≅LN in the question.
Here, we will prove the congruency of the given statement ST≅LR
Finally, using the given points and mathematical concepts we will conclude the final result.
We have SU≅LR
TU≅LN
Here, we have seen that T, and N are the midpoints of the lines SU,LR
Now, use each mathematical concept to prove ST≅LR
Using the given information
Hence, using the given statement
SU≅LR
TU≅LN
We prove that ST≅NR
Page 27 Problem 6 Answer
We are given a partially filled proof for the congruence of CD≅AB.
And it is given that, AB≅CD.
We are required to complete the proof.
Here, we will use properties of congruence to fill this.
We will compare the reasons and the statements to each other and then fill the given proof as,
We can fill the given proof as
Page 27 Problem 7 Answer
We are given that,AB≅DE
B is the midpoint of AC
E is the midpoint of DF
We are required to prove that, BC≅EF.
Here, we will use properties of congruence and equality to complete the given proof.
We will compare the reasons and the statements to each other and then fill the given proof as,
The given proof can be completed as,
Page 28 Problem 8 Answer
We are given a figure, in which the distance from Grays on to Apex is the same as the distance from Redding to Pine Bluff.
That is, GA≅RP.
We are required to prove that the distance from Grays on to Redding is equal to the distance from Apex to Pine Bluff. GR≅AP.
Here, we will use properties of equality to prove this.
The given statement can be proved as,
The proof of the distance from Grayson to Redding is equal to the distance from Apex to Pine Bluff is given by,