Mathematics: STATEMENT REASON 1.∠1 and ∠2 are supplementary angles 1. Given 2. m ∠1 + m ∠2 = 180° 2. 3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays 4. 4. 5. m ∠1 + m ∠2 = m ∠1 + m ∠3 5. 6. 6. 7. l || m

STATEMENT , №14097233, 31.01.2020 12:35

Mathematics

Complete the proof of the exterior angle theorem. given: ∠4 is an exterior angle of △abc. prove: m∠1+m∠2=m∠4 statement reason 1. ∠4 is an exterior angle of △abc. 1. 2. ∠3 and ∠4 form a linear pair. 2. 3. ∠3 is supplementary to ∠4. 3. 4. m∠3+m∠4=180° 4. 5. 5. triangle sum theorem 6. m∠1+m∠2+m∠3=m∠3+m∠4 6. 7. 7.

Step-by-step answer

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Step-by-step explanation:

Statement Reason

1. ∠4 is an exterior angle of ΔABC Given

2. ∠3 and ∠4 form a linear pair Linear pair property

3. ∠3 is supplementary to ∠4 Straight line property

4. m∠3+m∠4=180° ∠3 is supplementary to ∠4

5. m∠1+m∠2+m∠3=180° Triangle sum theorem

6.m∠1+m∠2+m∠3= m∠3+m∠4 Statement 4 and 5

7. m∠1+m∠2=m∠4 Subtraction property

Mathematics

Complete the proof of the exterior angle theorem. given: ∠4 is an exterior angle of △abc. prove: m∠1+m∠2=m∠4 statement reason 1. ∠4 is an exterior angle of △abc. 1. 2. ∠3 and ∠4 form a linear pair. 2. 3. ∠3 is supplementary to ∠4. 3. 4. m∠3+m∠4=180° 4. 5. 5. triangle sum theorem 6. m∠1+m∠2+m∠3=m∠3+m∠4 6. 7. 7.

Step-by-step answer

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Step-by-step explanation:

Statement Reason

1. ∠4 is an exterior angle of ΔABC Given

2. ∠3 and ∠4 form a linear pair Linear pair property

3. ∠3 is supplementary to ∠4 Straight line property

4. m∠3+m∠4=180° ∠3 is supplementary to ∠4

5. m∠1+m∠2+m∠3=180° Triangle sum theorem

6.m∠1+m∠2+m∠3= m∠3+m∠4 Statement 4 and 5

7. m∠1+m∠2=m∠4 Subtraction property

Mathematics

Statements: reasons: 1.) 1.) given 2.) ∠1 and ∠2 form a linear pair 2.) 3.) 3.) linear pair postulate 4.) m∠1+m∠3=180 4.) angle addition postulate 5.) 5.) given: m∠2 = m∠3 prove: ∠1 and ∠3 are supplementary.

Step-by-step answer

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The answer to your question is below

Step-by-step explanation:

I hope it helps you

1.- m ∠2 = m ∠ 3

2.- ∠1 and ∠ 2 are adjacent angles

3.- m∠1 + m∠2 = 180°

4.-

5.- ∠1 and ∠3 are supplementary linear pair angles are supplementary

Mathematics

Statements: reasons: 1.) 1.) given 2.) ∠1 and ∠2 form a linear pair 2.) 3.) 3.) linear pair postulate 4.) m∠1+m∠3=180 4.) angle addition postulate 5.) 5.) given: m∠2 = m∠3 prove: ∠1 and ∠3 are supplementary.

Step-by-step answer

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The answer to your question is below

Step-by-step explanation:

I hope it helps you

1.- m ∠2 = m ∠ 3

2.- ∠1 and ∠ 2 are adjacent angles

3.- m∠1 + m∠2 = 180°

4.-

5.- ∠1 and ∠3 are supplementary linear pair angles are supplementary

Mathematics

Match the reasons with the statements in the proof if the last line of the proof would be 6. ∠1 and ∠7 are supplementary by definition. given: s || t prove: 1, 7 are supplementary 1. s||t given 2. ∠5 and ∠7 are supplementary. exterior sides in opposite rays. 3. m∠5 + m∠7 = 180° definition of supplementary angles. 4. m∠1 = m∠5 substitution 5. m∠1 + m∠7 = 180° if lines are ||, corresponding angles are equal.

Step-by-step answer

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Following are steps to matches which can be defined as follows:

Given:

$\bold{s||t}$ $\bold{\angle\ 5 \ and\ \angle\ 7}$ are extra exterior sides in opposite beams. Supplementary angles were defined as: $\bold{m\ \angle\ 5 + m\ \angle\ 7 = 180^{\circ}}$ When lines are ||, corresponding angles are congruent: $\bold{m \ \angle 1 = m \ \angle 5 }$ Substitution: $\bold{m \angle 1 + m \angle 7 = 180^{\circ}}$

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Mathematics

Match the reasons with the statements in the proof if the last line of the proof would be 6. ∠1 and ∠7 are supplementary by definition. given: s || t prove: 1, 7 are supplementary 1. s||t given 2. ∠5 and ∠7 are supplementary. exterior sides in opposite rays. 3. m∠5 + m∠7 = 180° definition of supplementary angles. 4. m∠1 = m∠5 substitution 5. m∠1 + m∠7 = 180° if lines are ||, corresponding angles are equal.

Step-by-step answer

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23

Following are steps to matches which can be defined as follows:

Given:

$\bold{s||t}$ $\bold{\angle\ 5 \ and\ \angle\ 7}$ are extra exterior sides in opposite beams. Supplementary angles were defined as: $\bold{m\ \angle\ 5 + m\ \angle\ 7 = 180^{\circ}}$ When lines are ||, corresponding angles are congruent: $\bold{m \ \angle 1 = m \ \angle 5 }$ Substitution: $\bold{m \angle 1 + m \angle 7 = 180^{\circ}}$

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StudenGPT

Statements 1. Line I and line m intersect 2. 1 is supplementary to 2 3.? 4. 13 Reasons 1. given 2. linear pair theorem 3.? 4. congruent supplements theorem Which statement and reason best completes the proof? O A. Statement: 3. 3 is supplementary to *2; Reason: 3. linear pair theorem B. Statement: 3. m 1 + m 2 = 180º; Reason: 3. definition of supplementary angles O C. Statement: 3. 1 is supplementary to *4; Reason: 3. linear pair theorem D. Statement: 3. m 1 + m 3 = 180°; Reason: 3. definition of supplementary angles

Step-by-step answer

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To determine the correct statement and reason that best completes the proof, let's analyze the given statements and reasons step by step:

Statements:
1. Line I and line m intersect.
2. 1 is supplementary to 2.
3. ?
4. 13.

Reasons:
1. Given.
2. Linear pair theorem.
3. ?
4. Congruent supplements theorem.

We need to find the statement and reason that can logically complete the proof based on the information provided.

Statement 1 indicates that Line I and line m intersect. This information is given, and it doesn't provide any direct relation to the supplementary angles mentioned in statement 2.

Statement 2 states that 1 is supplementary to 2. It follows the Linear Pair Theorem, which says that if two angles form a linear pair, then they are supplementary. This statement is supported by the second reason, which is the Linear Pair Theorem.

Statement 4, which is unrelated to the missing statement 3, is simply the number 13 and doesn't contribute to the proof.

Now let's examine the options for the missing statement and reason:

Option A suggests:
Statement: 3. 3 is supplementary to *2;
Reason: 3. Linear pair theorem.

Option B suggests:
Statement: 3. m1 + m2 = 180º;
Reason: 3. Definition of supplementary angles.

Option C suggests:
Statement: 3. 1 is supplementary to *4;
Reason: 3. Linear pair theorem.

Option D suggests:
Statement: 3. m1 + m3 = 180°;
Reason: 3. Definition of supplementary angles.

To determine the best answer, we need to choose the option that aligns with the given information and follows logical reasoning.

Option A suggests that 3 is supplementary to "2," which is not mentioned or implied in the given statements. So, option A can be eliminated.

Option B suggests that the measure of angle 1 (m1) added to the measure of angle 2 (m2) equals 180 degrees. This aligns with statement 2, which states that 1 is supplementary to 2. The reason provided is the definition of supplementary angles, which also supports statement 2. Therefore, option B seems to be the best answer.

Option C suggests that 1 is supplementary to *4, which is not mentioned or implied in the given statements. So, option C can be eliminated.

Option D suggests that the measure of angle 1 (m1) added to the measure of angle 3 (m3) equals 180 degrees. This relation is not provided or implied in the given statements. Therefore, option D can be eliminated.

Based on the analysis above, the best answer is:
Statement: 3. m1 + m2 = 180º;
Reason: 3. Definition of supplementary angles.

This answer aligns with the given statements and reasons and provides a logical step in completing the proof.

Mathematics

question 1 - read the proof. given: m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100° prove: △hkj ~ △lnp statement reason 1. m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100° 1. given 2. m∠h + m∠j + m∠k = 180° 2. ? 3. 30° + 50° + m∠k = 180° 3. substitution property 4. 80° + m∠k = 180° 4. addition 5. m∠k = 100° 5. subtraction property of equality 6. m∠j = m∠p; m∠k = m∠n 6. substitution 7. ∠j ≅ ∠p; ∠k ≅ ∠n 7. if angles are equal then they are congruent 8. △hkj ~ △lnp 8. aa similarity theorem which reason is missing in step 2? a)cpctc b)definition of supplementary

Step-by-step answer

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Question 1
Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
To prove that: △HKJ ~ △LNP
Statement Reason

1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°   1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N    7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem

The reason that is missing in step 2 is triangle angle sum theorem.
The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180°.

Question 2
Given that △ABC is an isosceles triangle with legs AB and AC and △AYX is also an isosceles triangle with legs AY and AX.

To prove that △ABC ~ △AYX.
Statements    Reasons
1. △ABC is isosceles with legs AB and AC;
△AYX is also isosceles with legs AY and AX.    1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX    3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC / AB = AX 6. division property of equality
7. AY/AB = AX/AC 7. division property of equality
8. ? 8. ?
9. △ABC ~ △AYX    9. SAS similarity theorem

The statement and reason missing in the proof are ∠A ≅ ∠A; reflexive property
SAS Similarity or Side-Angle-Side similarity states that when two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, then the triangles are similar.

Question 3 -
Given that line RS intersects triangle BCD at two points and is parallel to segment DC.
The statements thet are correct is △BCD is similar to △BSR.

Mathematics

question 1 - read the proof. given: m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100° prove: △hkj ~ △lnp statement reason 1. m∠h = 30°, m∠j = 50°, m∠p = 50°, m∠n = 100° 1. given 2. m∠h + m∠j + m∠k = 180° 2. ? 3. 30° + 50° + m∠k = 180° 3. substitution property 4. 80° + m∠k = 180° 4. addition 5. m∠k = 100° 5. subtraction property of equality 6. m∠j = m∠p; m∠k = m∠n 6. substitution 7. ∠j ≅ ∠p; ∠k ≅ ∠n 7. if angles are equal then they are congruent 8. △hkj ~ △lnp 8. aa similarity theorem which reason is missing in step 2? a)cpctc b)definition of supplementary

Step-by-step answer

P Answered by PhD

111

Question 1
Given: m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°
To prove that: △HKJ ~ △LNP
Statement Reason

1. m∠H = 30°, m∠J = 50°, m∠P = 50°, m∠N = 100°   1. given
2. m∠H + m∠J + m∠K = 180° 2. ?
3. 30° + 50° + m∠K = 180° 3. substitution property
4. 80° + m∠K = 180° 4. addition
5. m∠K = 100° 5. subtraction property of equality
6. m∠J = m∠P; m∠K = m∠N 6. substitution
7. ∠J ≅ ∠P; ∠K ≅ ∠N    7. if angles are equal then they are congruent
8. △HKJ ~ △LNP 8. AA similarity theorem

The reason that is missing in step 2 is triangle angle sum theorem.
The triangle angle sum theorem states that the sum of the measures of the interior angles of a triangle is 180°.

Question 2
Given that △ABC is an isosceles triangle with legs AB and AC and △AYX is also an isosceles triangle with legs AY and AX.

To prove that △ABC ~ △AYX.
Statements    Reasons
1. △ABC is isosceles with legs AB and AC;
△AYX is also isosceles with legs AY and AX.    1. given
2. AB ≅ AC and AY ≅ AX 2. definition of isosceles triangle
3. AB = AC and AY = AX    3. definition of congruency
4. AY • AC = AX • AC 4. multiplication property of equality
5. AY • AC = AX • AB 5. substitution property of equality
6. AY • AC / AB = AX 6. division property of equality
7. AY/AB = AX/AC 7. division property of equality
8. ? 8. ?
9. △ABC ~ △AYX    9. SAS similarity theorem

The statement and reason missing in the proof are ∠A ≅ ∠A; reflexive property
SAS Similarity or Side-Angle-Side similarity states that when two triangles have corresponding angles that are congruent and corresponding sides with identical ratios, then the triangles are similar.

Question 3 -
Given that line RS intersects triangle BCD at two points and is parallel to segment DC.
The statements thet are correct is △BCD is similar to △BSR.

Mathematics

I ve been stuck on this problem forever now! provide reasons for the proof. given: angle 2=4 and 2 and 3 are supplementary prove: angle 1=3 statement: reason 1. 2=4 1. given 2. m2=m4 2. angle congruence postulate 3. angles 2 and 3 are supplementary 3. given 4. m2+m3=180 4. definition of supplementary angles 5. angles 1 and 4 are supplementary 5. fill in blank 6. m1+m4=180 6. definition of supplementary angles 7. m1+m4=m2+m3 7. fill in blank 8. m1+m4=m4+m3 8. fill in blank 9. m1=m3 9. fill in blank 10. 1=3 10. fill in blank

Step-by-step answer

P Answered by PhD

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Statement 1: ∠2=∠4 .. Given

Statement 2: Measure of angle 2 = Measure of angle 4 = Alternate angles

Statement 3: ∠2=∠3 , Given Supplementary Angles

Statement 4 : ∠2+∠3=180 , Sum of supplementary angles is equal to 180 degree.

Statement 5: ∠1 and ∠4 are supplementary angles because angle of a straight line is equal to 180 degree.

Statement 6: Measure of angle 1 + measure of angle 4 = 180, sum of angles of supplementary angles is 180 degree.

Statement 7: ∠1+∠4= ∠2+∠3 ... Both sums are 180 degrees.

Statement 8: ∠1+∠4=∠4+∠3 .. ∠2 and ∠4 are equal (alternate angles)

Statement 9: ∠1= ∠3 , because ∠4 is common on both sides.

Statement 10: ∠1 = ∠3 .. hence, proved

STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m ∠1 + m ∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m ∠1 + m ∠2 = m ∠1 + m ∠3 5.
6. 6.
7. l || m 7.

Faq

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STATEMENT REASON 1.∠1 and ∠2 are supplementary angles 1. Given 2. m ∠1 + m ∠2 = 180° 2. 3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays 4. 4. 5. m ∠1 + m ∠2 = m ∠1 + m ∠3 5. 6. 6. 7. l || m 7.

Faq

Try asking the Studen AI a question.

STATEMENT REASON
1.∠1 and ∠2 are supplementary angles 1. Given
2. m ∠1 + m ∠2 = 180° 2.
3. ∠1 and ∠3 are supplementary angles 3. Exterior sides in opposite rays
4. 4.
5. m ∠1 + m ∠2 = m ∠1 + m ∠3 5.
6. 6.
7. l || m 7.