How do you construct congruent segments, segment bisectors, angles, and angle bisectors using tools such as a compass and straightedge?

Answer and Step-by-step explanation: Congruent segments are lines with the same size and shape. Bisector means divide something in half.

1) Use a straightedge and draw a segment.

2) Measure this line you created.

3) Draw another line with the same measurement than the first one.

4)You have 2 congruent segments.

1) Draw a segment;

2) Find the midpoint of this segment: measure the segment and divide the number by 2;

3) Measure the midpoint from one end. This point will be in the middle of the segment;

4) Draw a point there;

5) Lastly, draw a line passing through the midpoint and intersecting the segment;

1) Using a straightedge, draw two lines connecting one another in only one point;

2) Open the compass with the same openness you draw your two segment;

3) Put the compass needle in the point which connects the 2 lines;

4) Put the pencil of the compass on one of the segment;

5) Draw a curve towards the other line;

6) That's the angle;

1) Follow the same rules to create an angle;

2) After creating an angle, open the compass in any width;

3) With the needle tip on the point where the segments crosses, mark a point on each segment;

4) With any openness of the compass, put the needle point on the point you just created and draw a curve;

5) Do the same as 4 for the other point;

6) Using straightedge, draw a line connecting the point where the segments meet and the point created by 4 and 5;

7) This is an angle bisector;

x = ±sqrt(10)

step-by-step explanation:

5 - 2x² = -15

subtract 5 from each side

5-5 - 2x² = -15-5

-2x^2   = -20

divide by -2 on each side

-2x^2   /-2= -20/-2

x^2 =10

take the square root on each side

sqrt(x^2 )=±sqrt(10)

x = ±sqrt(10)

check:

5 - 2x² = -15

+sqrt(10)

5 - 2(sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15

-sqrt(10)

5 - 2(-sqrt(10))² = -15

5 -2(10) = -15

5 -20 = -15

-15 = -15