Anonymous
Anonymous asked in Education & ReferenceHomework Help · 6 years ago

If you would just check my answers for me that would be amazing! If I miss anything up please explain to me how to do it! THANKS A TON :)

1. If quadrilateral ACEG is congruent to quadrilateral MNPR with the congruence statement in corresponding order, then which of the following is true? (Points : 5)

Segment AG is congruent to segment MR.

Segment AC is congruent to segment MR.

Segment CE is congruent to segment PR.

Segment EG is congruent to segment MN.---- my answer

Question 2. Given that segment QS is congruent to segment RP and segment PQ is congruent to segment SR, which theorem or postulate proves PRS is congruent to SQP?

(Points : 5)

HL Congruence Theorem

SSS Congruence Postulate

SAS Congruence Postulate. ----- My answer

ASA Congruence Postulate

Question 3. Given that segment ST is parallel to segment YX and segment ST is congruent to segment YX, which theorem or postulate proves STW is congruent to YXW?

(Points : 5)

HL Congruence Theorem

SSS Congruence Postulate ----- my answer

SAS Congruence Postulate

ASA Congruence Postulate

Question 4. Given that segment AC is congruent to segment CE and segment BC is congruent to segment DE, which theorem or postulate proves ABC is congruent to CDE?

(Points : 5)

HL Congruence Theorem ---- my answer

ASA Congruence Postulate

SAS Congruence Postulate

SSS Congruence Postulate

Question 5. What is m A?

(Points : 5)

39.5°

40.5°

49.5°

139.5°

Question 6. What is the measure of the vertex angle of an isosceles triangle if one of its base angles measures 34° and its congruent sides each measure 15 cm? (Points : 5)

56°

68°

112°

Question 7. To prove that ABCD is a parallelogram, you would have to first prove ACD is congruent to CAB by using which of the following?

(Points : 5)

SSS Congruence Postulate ---- my answer

SAS Congruence Postulate

ASA Congruence Postulate

AAS Congruence Theorem

Question 8. To prove that the diagonals of rectangle QRPN are congruent, you can use CPCTC after you prove which of the following?

(Points : 5)

PNQ is congruent to NPR by the SAS Congruence Postulate. ---- my answer

QRP is congruent to PNQ by the HL Congruence Theorem.

NQR is congruent to RPN by the SSS Congruence Postulate.

QRP is congruent to PNQ by the SSS Congruence Postulate.

Question 9. Which is true about the diagonals of a rectangle? (Points : 5)

They are always congruent.

They do not bisect each other.

They are always perpendicular. ----- my answer

They are sometimes congruent.

Question 10. If the diagonals of a parallelogram are congruent and are perpendicular bisectors of each other, then the parallelogram is which of the following? (Points : 5)

rectangle

square

trapezoid

Question 11.. What is the measure of a base angle of an isosceles triangle if its vertex angle measures 80°? (Points : 5)

100°

80°

25°

Question 12.Which of the following lengths could be the sides of a triangle? (Points : 5)

5 cm, 17 cm, 12 cm ---- my answer

13 cm, 23 cm, 10 cm

18 cm, 7 cm, 14 cm

22 cm, 14 cm, 5 cm

Relevance

1)

Segment AG is congruent to segment MR.

Note that when we say ABCD is congruent to EFGH, there is a direct "letter congruency".

This means AB must be congruent to EF; BC to FG; CD to GH... etc.

2)

SSS Congruence Postulate

Note that 2 sides are said to be congruent.

The third side happen to be a common side (PS), so it is obvious that this side will be congruent as well. Hence, we can apply SSS.

3)

ASA Congruence Postulate

Note that angle TSW = angle XYW and angle STW = angle YXW due to alternate interior angles, which we could apply as ST is parallel to YX.

It is also given that ST is congruent to YX, so we can apply ASA.

4)

HL Congruence Theorem

This is clear since the corresponding hypotenuse and a corresponding leg are congruent.

5)

In any case, this is an isosceles triangle.

Thus, you can subtract the given angle from 180 degrees, and then divide the resulting angle by 2.

6)

180 - 34 - 34

= 112 degrees

The length is just there to confuse you.

One base angles is 34 degrees, the other base angle must also be 34 degrees since this is an isosceles triangle. Thus, we just subtract 34 degrees twice from 180 degrees, which is the sum of the interior angles of a triangle.

7)

AAS Congruence Theorem

Note that two pairs of congruent angles have been given.

AC is a common side, so clearly it is congruent as well for both triangles.

There is no evidence or information given to point out that any of the other sides are congruent.

Thus we can apply only AAS.

8)

PNQ is congruent to NPR by the SAS Congruence Postulate

Clearly you can't use SSS or HL here, since you are trying to prove the diagonals are equal.

If you use SSS or HL, you will be assuming that the diagonals are equal even before proving it is true.

9)

They are always congruent.

You just proven this in question 8).

10)

square

Note that while a rhombus have perpendicular bisecting diagonals, the diagonals are not congruent.

11)

(180 - 80) / 2

= 100 / 2

= 50 degrees

12)

18cm, 7cm, 14cm

Note that the sum of the two shorter sides of a triangle must always be longer than the longest side.

If the two shorter sides add up to the longest side, you will just have a flat straight line consisting of all three sides.

If the two shorter sides add up to less than the longest side, these two sides cannot possibly meet each other.

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• 1)

Segment AG is congruent to segment MR.

2)

SSS Congruence Postulate.

because seg. PS ≅ seg. PS by Reflexive prop. of ≅.

3)

ASA Congruence Postulate

4)

HL Congruence Theorem ---- my answer

5)

m ∠ A is same as m ∠ B since it is isosceles triangle.

x + x + 99° = 180°

2x = 180° - 99°

2x = 81°

x = 40.5°

6)

34° + 34° + vertex = 180° ----> vertex = 112°

7)

AAS Congruence Theorem

8)

PNQ is congruent to NPR by the SAS Congruence Postulate. ---- my answer

9)

They are always congruent.

10)

square

11)

true

12)

18 cm, 7 cm, 14 cm

18 + 7 > 14 True

18 + 14 > 7 True

14 + 7 > 18 True

Hope it helps

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