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sashaice [31]
3 years ago
10

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 ar

e congruent because they are vertical angles. Then, by which property are angles 4 and 5 congruent? Together, these statements prove which theorem? A) Transitive Property of Congruency; If parallel lines have a transversal, then supplemental angles are congruent. B) Transitive Property of Congruency;If parallel lines have a transversal, then alternate interior angles are congruent. C) Symmetric Property of Congruency; If parallel lines have a transversal, then alternate exterior angles are congruent. D) Commutative Property of Congruency; If parallel lines have a transversal, then same side interior angles are congruent.
Mathematics
2 answers:
tiny-mole [99]3 years ago
7 0

Answer:

Transitive Property of Congruency;If parallel lines have a transversal, then alternate interior angles are congruent.

The Transitive Property of Congruency:

If 2 angles are congruent to a third angle, then they are congruent to each other. So, since angles 4 and 5 are both congruent to angle 1, they are congruent to each other.

Angles 4 and 5 are alternate interior angles. Therefore, if parallel lines have a transversal, alternate interior angles are congruent.

Makovka662 [10]3 years ago
6 0

Answer:

Option B)

Step-by-step explanation:

Given :

Given that lines a and b are parallel, angles 1 and 5 are congruent because they are corresponding angles, and angles 1 and 4 are congruent because they are vertical angles

To find : by which property are angles 4 and 5 congruent

Solution :

We know that if two parallel lines are cut by a transversal, then the pairs of alternate interior angles are congruent.

Also, we know that if two things are equal to the same thing then they are equal to each other . In this case, we can say that if two angles are congruent to a third angle, then they are congruent to each other. As angles 4 and 5 are both congruent to angle 1, they are congruent to each other but angles 4 and 5 are alternate interior angles. So, if parallel lines have a transversal, alternate interior angles are congruent.

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vovangra [49]

Answer:

The other side = 13 feets long

Step-by-step explanation:

Given that :

Scale of drawing : 2 inches represents 5 feets

Area of rectangular room according to scale drawing = 24.96 in²

Length of one side of the room = 12 feets

Length of other side = x

Area of rectangle = Length * width

If :

2 inches = 5 feets

x = 12 feets

x = (12 *2) / 5

x = 4.8 inches

Hence,

For the scaled drawing :

4.8 * width = 24.96

Width = 24.96 / 4.8

Width = 5.2 inches

Converting to feets according to scale:

2 inches = 5 feets

5.2 inches = x feets

x = (5.2 * 5 ) / 2

x = 13 feets

Other side is 13 feets long

4 0
3 years ago
3. Please show your work to find the mean and standard deviation of the data. Round to the nearest tenth.
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3 years ago
Two spherical shells have their mass uniformly distrubuted over the spherical surface. One of the shells has a diameter of 2 met
ivann1987 [24]
The moment of inertia of a spherical shell is I = mr²

If two spheres have the same moment of inertia, then
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m₂ = m₁ (r₁/r₂)²

Given m₁ = 1 kg, r₁ = 2 m, r₂ = 1m,
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3 years ago
The height of a parallelogram is three times its base. If the area is 972 square inches, what is the base and height?
Fed [463]
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8 0
3 years ago
I’m not to sure on how to find CEB can someone explain how to find it and what the answer would be,please
lakkis [162]

Answer:

m∠CEB is 55°

Step-by-step explanation:

Since ∠ADE = 55°, and ∠ADE is half of ∠ADC because ED bisects ∠ADC. Bisect means to cut in half.

∠ADC = 110° because it is double of ∠ADE.

Since AB║CD and AD║BC, the two sets of parallel lines means this shape is a parallelogram. In parallelograms, <u>opposite angles have equal measures</u>.

∠ADC = ∠CBE = 110°

All quadrilaterals have a sum of angles 360°. Since ∠DCB = ∠BAD and we know two of these other angles are each 110°:

360° - 2(110°) = 2(∠DCB)

∠DCB = 140°/2

∠DCB = ∠BAD = 70°

∠DCB was bisected by EC, which makes each divided part half.

∠DCE = ∠BCE = (1/2)(∠DCB)

∠DCE = ∠BCE = (1/2)(70°)

∠DCE = ∠BCE = 35°

All triangles' angles sum to 180°.

In ΔBCE, ∠BCE = 35° and ∠CBE = 110°.

∠CEB = 180° - (∠BCE + ∠CBE)

∠CEB = 180° - (35° + 110°)

∠CEB = 55°

Therefore m∠CEB is 55°.

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3 years ago
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