Mathematics, 14.02.2020 18:52 whitakers87

Similarity/Proofs Sample Work

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Answer from: gogo16732

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Step-by-step explanation:

Q1. Statement Reason

1. $T \text{ is the midpoint of }\overline{QR}\\ \\U \text{ is the midpoint of }\overline{QS}\\ \\V \text{ is the midpoint of }\overline{RS}\\ \\$ Given

2. $\overline{TV}, \overline{TU}, \overline{UV}\text{ are midsegments}$ Midsegments connect midpoints of opposite sides

3. $\overline{TU}=\dfrac{1}{2}\overline{RS}\\ \\\overline{UV}=\dfrac{1}{2}\overline{QR}\\ \\\overline{VT}=\dfrac{1}{2}\overline{SQ}$ Triangle midsegment theorem

4. $\dfrac{\overline{TU}}{\overline{RS}}=\dfrac{1}{2},\\ \\\dfrac{\overline{UV}}{\overline{QR}}=\dfrac{1}{2},\\ \\\dfrac{\overline{VT}}{\overline{SQ}}=\dfrac{1}{2}$ Division property of equality

5. $\dfrac{\overline{TU}}{\overline{RS}}=\dfrac{\overline{UV}}{\overline{QR}}=\dfrac{\overline{VT}}{\overline{SQ}}$ Transitive property

6. $\triangle QRS\sim \triangle VUT$ SSS similarity theorem

Q2. Statement Reason

1. $\overline {LM}\perp \overline {MO},\\ \\\overline {PN}\perp \overline {MO}$ Given

2. $\angle ONP, \ \angle OML\text{ are right angles}$ Definition of perpendicular

3. $\angle ONP\cong \angle OML$ All right angles are congruent

4. $\angle O\cong \angle O$ Reflexive property

5. $\triangle LMO\cong \triangle PNO$ AA similarity theorem

Q3. Statement Reason

1. $ABCD\text{ is a trapezoid}$ Given

2. $\overline{AD}\parallel \overline{BC}$ Definition of trapezoid

3. $\angle ADE\cong \angle CBD$ Alternate interior angles are congruent (Alternate interior angles theorem)

4. $\angle DAC\cong \angle ACB$ Alternate interior angles are congruent (Alternate interior angles theorem)

5. $\triangle AED\sim \triangle CEB$ AA similarity theorem

Q4. Statement Reason

1. $\overline{AC}\text{ and }\overline{EC}\text{ intersect at} B$ Given

2. $\angle ABE\cong \angle CBD$ Vertical angles theorem

3. $\dfrac{\overline {BC}}{\overline{EB}}=\dfrac{5}{15}=\dfrac{1}{3}$ Proportion of corresponding sides

4. $\dfrac{\overline {BD}}{\overline{AB}}=\dfrac{4}{12}=\dfrac{1}{3}$ Proportion of corresponding sides

5. $\dfrac{\overline{BC}}{\overline{EB}}=\dfrac{\overline{BD}}{\overline{BA}}$ Transitive property

6. $\triangle ABE\sim \triangle DBC$ SAS similarity theorem

Answer from: Quest

4.0 ft

step-by-step explanation:

4.0 ft

Answer from: Quest

The answer is 8 apex

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