Your solution for the first problem is correct. If EF = 15 and the scale factor is 5/2, then JK = 6.
For the second problem, the proof is mostly correct, but there are a few minor things that need to be fixed or clarified:
1) Instead of stating "<1 is congruent to <2" twice in the Statements column, you should state "1.Given" and "8. <1 is congruent to <2" in the Reasons column.
2) In statement 5, it should be "m<DAB = m<BCA" instead of "m<BCD"
3) In statement 6, it should be "If <1 is congruent to <2 and <1 is congruent to <3, then <2 is congruent to <3" in the Reasons column.
4) In statement 8, it should be "<CAB is congruent to <CBD" or "<DAB is congruent to <BCA" instead of "<1 and <2"
Here is the modified proof:
PROOF
Statements Reasons
1. ABCD is a parallelogram 1. Given
2. <1 is congruent to <2 1. Given
3. Draw segment from A to C 3. Two points determine exactly one line
4. < 1 & <3 are congruent 4. Alternate angles are congruent
5. AC bisects angle 1 & 2 5. Def. of Angle bisector
6. m<DAB = m<BCA 6. Opposite angles in a parallelogram are equal
7. <2 is congruent to <3 7. If <1 is congruent to <2 and <1 is congruent to <3, then <2 is congruent to <3
8. <CAB is congruent to <CBD 8. Cor.parts are equal
9. AB=BC=CD=DA 9. Sides opposite congruent angles are congruent
10. ABCD is a rhombus 10. A parallelogram with consecutive sides congruent is a rhombus
Can some one please check these for me.Thanks
Angle DEF is similar to Angle HJK and the scale factor of angle DEF to anle HJK IS 5/2. If EF =15 FIND JK
Here is what I came up with Am I correct
5/2 = EF/JK
5/2 =15/JK
5(JK)=30
JK=30/5
JK=6
Given: ABCD is a parallelogram; <1 is congruent to <2
To Prove: ABCD is a Rhombus
Plan: Show <2 is congruent to < CAB.
hence CB is congruent to AB,
making ABCD a parallelogram
with consecutive sides congruent
PROOF
Statements Reasons
1. ABCD is a parallelogram 1.Given
<1 is congruent to <2
2. Draw segment from A to C 2. Two points determine exactly one line
3.< 1 & <3 are congruent 3. Alternate angles are congruent
4. AC bisects angle 1&2 4. Def. of Angle bisector
5 . m<DAB=m<BCD 5. Opposite angles in a parallelogram are equal
6. <2 & <3 are congruent 6. Transitive prop 7 . AB=BC 7. Sides oposite are congruent angles
8.<1 & <2 8. Cor.parts are eual
9. AB=BC=CD=DA 9. ABCD is a rhombus
1 answer
1 answer