Geometry

posted by .

Please help

1. If segment LN is congruent to segment NP and ∠1 ≅ ∠2, prove that ∠NLO ≅ ∠NPM:

Overlapping triangles LNO and PNM. The triangles intersect at point Q on segment LO of triangle LNO and segment MP of triangle PNM.

Hector wrote the following proof for his geometry homework for the given problem.


Statements Reasons
segment LN is congruent to segment NP Given
∠1 ≅ ∠2 Given
∠N ≅ ∠N Reflexive Property
ΔLNO ≅ ΔPNM
∠NLO ≅ ∠NPM Corresponding Parts of Congruent Triangles Are Congruent


Which of the following completes Hector's proof?
Angle-Angle-Side Postulate***
Angle-Side-Angle Postulate
Side-Angle-Side Postulate
Side-Side-Side Postulate

2. Use the figure below to answer the question that follows:

Intersecting triangles ACE and BDF. They intersect at points G, H, I, and J.

What must be given to prove that ΔBJI ~ ΔCJG?

segment BH is congruent to segment CH and segment BG is congruent to segment CI
∠BIJ ≅ ∠CGJ and ∠JBI ≅ ∠JIB
segment BI is congruent to segment CG and segment JI is congruent to segment JG
∠BIJ ≅ ∠CGJ and ∠BJI ≅ ∠CJG***

3. Abdul is making a map of his neighborhood. He knows the following information:

His home, the middle school, and high school are all on the same street.
His home, the elementary school, and his friend's house are on the same street.
The angle between the elementary school, middle school, and his home is congruent to the angle between his friend's house, the high school, and his home.


A street map is shown. The streets form a triangle comprised of the locations of home, friends house, and the high school. The triangle is intersected by a line formed by the elementary and middle school.

What theorem can Abdul use to determine that certain angles are congruent?
Corresponding Angles Theorem***
Vertical Angles Theorem
Pythagorean Theorem
Angle-Angle-Side Theorem

4.The figure below shows triangle NRM with r2 = m2 + n2:

Triangle NRM has legs m and n, and r is the length of its longest side.

Ben constructed a right triangle EFD with legs m and n, as shown below:

Triangle EFD has legs m and n and hypotenuse f.

He made the following table to prove that triangle NRM is a right triangle:


Statement Reason
1. r2 = m2 + n2 Given
2. f2 = m2 + n2 Pythagorean Theorem
3. f2 = r2 Substitution
4. f = r Square Root Property of Equality
5. Triangle NRM is congruent to triangle EFD ?
6. Angle NRM is a right angle CPCTC
7. Triangle NRM is a right triangle Angle NRM is a right angle

Which reason best fits statement 5?
SSS Postulate
SAS Postulate***
AAA Postulate
AAS Postulate

  • Geometry -

    Wait, #4 is SSS Postulate, right?

  • Geometry -

    Anyone, please?

  • Geometry -

    Correct.



    I hope.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    given: segment AB is paralell to segment DC; segment AB is congruent to segment to DC prove: triangle ABC is congruent to triangle CDA statements: 1. segment AB is congruent to segment DC 2.segment AC is congruent to segment AC 3.segment …
  2. Geometry

    Yes, I'm this desperate. I just have problems with coming up with the statements for two column proofs. Answers would be appreciated. Given: line segment AX congruent to line segment DX, line segment XB is congruent to XC. Prove: Line …
  3. math

    Given: segment AC and segment BD bisect each other at E prove: E is the midpoint of segment RS i don't know if you will be able to visualize the picture but just incase someone is i really need help on the proof for this one. Picture: …
  4. Geometry

    Please write a paragraph proof for this statement. 30: Point Y is the midpoint of segment XZ. Z is the midpoint of segment YW. PRove that segment or line XY is congruent to segment or line ZW.
  5. Geometry

    Please write a paragraph proof for this statement. Point Y is the midpoint of segment XZ. Z is the midpoint of segment YW. PRove that segment or line XY is congruent to segment or line ZW.
  6. geometry

    Prove that you have constructed point C on segment EF such that angle ACE is congruent to angle BCF. (Points A and B are on the same side of segment EF, but have different distances to the segment.) I am not sure if I am on the right …
  7. geometry

    I need to figure out this proof, the figure is two triangles forming a rhombus. Given: segment BD is the angle bisector of triangle ABC and triangle ADC Prove: Triangle ABD is congruent to Triangle CBD So far I have segment BD is the …
  8. Geometry

    According to the given information, segment AB is parallel to segment DC and segment BC is parallel to segment AD.. Construct diagonal A C with a straightedge. It is congruent to itself by the Reflexive Property of Equality. ________________. …
  9. geometry

    given: segment HI congruent to segment GJ, segment HI parallel to segment GJ prove: triangle GJH congruent to triangle IHJ
  10. Geometry

    Theorem: A line parallel to one side of a triangle divides the other two proportionately. In the figure below, segment DE is parallel to segment BC and segment EF is parallel to AB: The figure shows triangle ABC with segments DE and …

More Similar Questions