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Dimas [21]
3 years ago
15

In ΔABC shown below, line segment AB is congruent to line segment BC:

Mathematics
2 answers:
yan [13]3 years ago
6 0

Answer:

∠ABD ≅ ∠CBD

Step-by-step explanation:

<u>Given: </u>line segment AB ≅ line segment BC

<u>Prove:</u> The base angles of an isosceles triangle are congruent.

        Statement                                                         Reason

1.  Segment BD is an angle bisector of ∠ABC - By construction

2. ∠ABD ≅ ∠CBD -                                         Definition of an Angle Bisector

3. Segment BD ≅ segment BD -                       Reflexive Property

4. ΔABD ≅ ΔCBD -                                         Side-Angle-Side (SAS) Postulate

5. ∠BAC ≅ ∠BCA -                                                       CPCTC

alisha [4.7K]3 years ago
6 0

Answer:

It is ABD = CBD I just got it right!

Step-by-step explanation:

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3 years ago
Use always, sometimes or never to make a true statement:
viva [34]

Answer:

1. Intersecting lines are <u>always</u> coplanar

2. Two planes <u>never</u> intersect in exactly one point

3. Three points are <u>always</u> coplanar

4. A plane containing two points of a line <u>always</u> contains the entire line

5. Four points are <u>sometimes</u> coplanar

6. Two lines <u>never</u> meet in more than one point.

7. Two skew lines are <u>never</u> coplanar

8. Line TQ and Line QT are <u>always</u> the same line.

Step-by-step explanation:

Note: Coplanar means "In the same plane"

1. Each line exist in many planes. But different lines must share at least one plane for them to intersect. That is why intersecting lines are always coplanar.

2. Two planes never intersect at exactly one point because only lines intersect at a point. Planes can only intersect along a line.

3.Three points are always coplanar because in geometry, a group of points are coplanar because there is a geometric plane that they all lie on.

4. A plane containing two points of a line always contains the entire line. Yes

5. Four points are only sometimes coplanar because there is a probability that they may all not lie on the same plane

6. Two lines never meet in more than one point because lines are basically straight and cannot bend over to intersect at another point

7. Two skew lines are never coplanar because skews lines are lines that do not intersect and are never parallel.

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3 years ago
Which rule can be used to find the output numbers in this table?
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3 0
3 years ago
Now there is a square city of unknown size with a gate at the center of each side. There is a tree 20 b from the north gate. Tha
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Answer:

The length of each side of the city is 250b

Step-by-step explanation:

Given

a = 20 --- tree distance from north gate

b =14 --- movement from south gate

c = 1775 --- movement in west direction from (b)

See attachment for illustration

Required

Find x

To do this, we have:

\triangle ADE \sim \triangle ACB --- similar triangles

So, we have the following equivalent ratios

AE:DE = AB:CB

Where:

AE = 20\\ DE = x/2 \\ AB = 20 + x + 14 \\ CB = 1775

Substitute these in the above equation

20:x/2 = 20 + x + 14: 1775

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Express as fraction

\frac{20}{x/2} = \frac{x + 34}{1775}

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Cross multiply

x *(x + 34) = 1775 * 40

Open bracket

x^2 + 34x = 71000

Rewrite as:

x^2 + 34x - 71000 = 0

Expand

x^2 + 284x -250x - 71000 = 0

Factorize

x(x + 284) -250(x + 284)= 0

Factor out x + 284

(x - 250)(x + 284)= 0

Split

x - 250 = 0 \ or\ x + 284= 0

Solve for x

x = 250 \ or\ x =- 284

x can't be negative;

So:

x = 250

6 0
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