Look at the figure shown below: A triangle RPQ is shown. S is a point on side PR and T is a point on side PQ. Points S and T are joined using a straight line. Nora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 45. Statement Reason 1. Segment ST is parallel to segment RQ Given 2. Angle QRS is congruent to angle TSP Corresponding angles formed by parallel lines and their transversal are congruent 3. Angle SPT is congruent to angle RPQ Reflexive property of angles 4. Triangle SPT is similar to triangle RPQ Angle-Angle Similarity Postulate 5. 60: (60+x) = Corresponding sides of similar triangles are in proportion Which of the following can she use to complete statement 5? a 60:(48 + 36) b 60:36 c 48:36 d 48:(48 + 36)

Question

jilliansgodfrey jilliansgodfrey

25-07-2020
Mathematics

contestada

Look at the figure shown below: A triangle RPQ is shown. S is a point on side PR and T is a point on side PQ. Points S and T are joined using a straight line. Nora is writing statements as shown to prove that if segment ST is parallel to segment RQ, then x = 45. Statement Reason 1. Segment ST is parallel to segment RQ Given 2. Angle QRS is congruent to angle TSP Corresponding angles formed by parallel lines and their transversal are congruent 3. Angle SPT is congruent to angle RPQ Reflexive property of angles 4. Triangle SPT is similar to triangle RPQ Angle-Angle Similarity Postulate 5. 60: (60+x) = Corresponding sides of similar triangles are in proportion Which of the following can she use to complete statement 5? a 60:(48 + 36) b 60:36 c 48:36 d 48:(48 + 36)

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maforchrist maforchrist · Answer 1 · 2020-07-25T16:14:58+02:00

maforchrist maforchrist

25-07-2020

Answer:

d:48:(48+36)

Step-by-step explanation:

cause the length PT corresponds to PQ so the value of PT which is 48 corresponds with the value of PQ which is 48+36 I guess

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astha8579 astha8579 · Answer 2 · 2022-01-06T10:49:19+01:00

Option d 48:(48+36) is the correct option.

Given that:

Statements that Nora wrote are:

Statement Reason

1. Segment ST is parallel to segment RQ Given

2. Angle QRS is congruent to angle TSP Corresponding angles formed by parallel lines and their transversal are congruent

3. Angle SPT is congruent to angle RPQ Reflexive property of angles

4. Triangle SPT is similar to triangle RPQ Angle-Angle Similarity Postulate

5. 60: (60+x) = ?

It is the property that a line intersecting and cutting a triangle which is parallel to a side of that triangle has those cuts with proportionate measures.

In the given figure, the above fact is shown symbolically as:

[tex]\dfrac{PS}{PR} = \dfrac{PT}{PQ}\\[/tex]

Thus we have :

[tex]\dfrac{60}{60+x} = \dfrac{48}{48+36}\\[/tex]

Thus Option d 48:(48+36) is the correct option.

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