(01.07 MC) Lines BC and ED are parallel. They are intersected by transversal AE, in which point B lies between points and E. The
y are also intersected by transversal EC. Angle ABC measures 70 degrees. Angle CED measures 30 degrees. Given: line BC is parallel to line ED m∠ABC = 70° m∠CED = 30° Prove: m∠BEC = 40° Statement Justification line BC is parallel to line ED Given m∠ABC = 70° Given m∠CED = 30° Given m∠BEC + m∠CED = m∠BED Angle Addition Postulate m∠BEC + 30° = 70° Substitution Property of Equality m∠BEC = 40° Subtraction Property of Equality Which of the following accurately completes the missing statement and justification of the two-column proof? m∠ABC = m∠CED; Corresponding Angles Theorem m∠ABC = m∠CED; Alternate Interior Angles Theorem m∠ABC = m∠BED; Corresponding Angles Theorem m∠ABC = m∠BED; Alternate Interior Angles Theorem
2 answers:
Answer:
m∠ABC = m∠BED; Corresponding Angles Theorem
Step-by-step explanation:
<u>Given:</u> line BC is parallel to line ED m∠ABC = 70° m∠CED = 30°
<u>Prove:</u> m∠BEC = 40°
Statement Justification
1. line BC is parallel to line ED - Given
2. m∠ABC = 70° - Given
3. m∠CED = 30° - Given
4. m∠BEC + m∠CED = m∠BED - Angle Addition Postulate
5. m∠ABC = m∠BED - Corresponding Angles Theorem
6. m∠BEC + 30° = 70° - Substitution Property of Equality
7. m∠BEC = 40° Subtraction Property of Equality
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the composite figure is just a trapezoid sitting on top of a rectangle
and then, the rectangle has a triangular hole in it
so.. get the area of the trapezoid
then get the area of the rectangle, which is just a 12x14
and then get the area of the triangle, which surely you know is 1/2 bh
then, subtract the triangle's area from the rectangle's area
and whatever is left, namely the difference, add that to the area of the trapezoid, and that's the composite's area
namely the area of the trapezoid plus the rectangle's, minus the triangle's
the composite figure is just a trapezoid sitting on top of a rectangle
and then, the rectangle has a triangular hole in it
so.. get the area of the trapezoid
then get the area of the rectangle, which is just a 12x14
and then get the area of the triangle, which surely you know is 1/2 bh
then, subtract the triangle's area from the rectangle's area
and whatever is left, namely the difference, add that to the area of the trapezoid, and that's the composite's area
namely the area of the trapezoid plus the rectangle's, minus the triangle's
Answer:
slope of EF=
∠QSR=45°,
∠PTQ=90°
if RT=24
then SQ=48
square is always a rectangle
∠SUT=21°
Step-by-step explanation:
two line are perpendicular to each other if product of their slope equal to -1
=-1
slope of HE==-
slope of EF=
slope of EF=-1=
slope of EF= answer
∠QSR=45°,
∠PTQ=90°
if RT=24
then SQ=48
square is always a rectangle
given ∠SUT=3x+6
∠RUS=5x-4
∠SUT=∠RUS
3x+6=5x-4
x=5
∠SUT=3x+6=15+6=21°
∠SUT=21°