Geometry help. questions I don't understand.?

Question

1). An isosceles triangle is _________________ an equilateral triangle.

a. Sometimes

b. Always

c. Never

2). An equilateral triangle is ______________ an isosceles triangle.

a. Sometimes

b. Always

c. Never

3). Triangle ABC is an isoceles triangle with line AB congruent to line AC. The measure of <A is 40 degrees. Find the measure of the angle opposite line AB.

http://i33.tinypic.com/312czl0.jpg

a. 40

b. 60

c. 140

d. 70

3). If triangle XYZ is equilateral and m<Y = 4/3x+20, then find the value of x.

a. 30

b. 80

c. 50

d. 60

4). Triangle ABC is an equilateral triangle. Find the value of x.

http://i33.tinypic.com/30jk40p.jpg

a. 10

b. 50

c. 60

d. 170

5). Triangle ABC is isosceles with line AC congruent to line BC. Solve for x.

http://i35.tinypic.com/311s5ls.jpg

a. 5

b. -1

c. 2

d. 5

6). Triangle ABC is isosceles. Find the measure of <A.

http://i33.tinypic.com/2l8gdgp.jpg

A. 20

B. 100

C. 160

D. 80

7). Triangle XYZ is isosceles. The base angles, <X and <Y, are four times the measure of the vertex angle, <Z. Find the measure of <X.

a. 20

b. 60

c. 80

d. 40

8). Find the measure of <Y.

http://i33.tinypic.com/15grnmr.jpg

a. 55

b. 110

c. 125

d. 70

Answer 1

I hate just giving people the answers for their homework, so instead of doing that I&#039;m going to just help you get off on the right path.

This website is a great reference for your isosceles triangle questions: http://mathworld.wolfram.com/IsoscelesTr...

For questions 1 and 2, the answer is actually written out for you on that page, so be sure to read carefully!

For question 3, consider the properties of an isosceles triangle. When two sides of a triangle have the same length (i.e. defining it as isosceles) then there are two equal angles. Therefore, using that property and knowing that angle A measures 40 degrees, you need to determine which angles are the ones with equal measures (hint: Triangle ABC is similar to the triangle on the other site I linked you to, so you can use the other site to find out which angles are congruent, and those are the same ones with equal measure on triangle ABC). Then you need to deduce the measure of the remaining angles, knowing that all of the angles inside of a triangle add up to 180 degrees.

For your second question 3 (:P), you make use of a special property of equilateral triangles. See if you can figure out a special property regarding the angles of the triangle by looking at the figure on this page: http://mathworld.wolfram.com/Equilateral... (Hint: What do the angles of the equilateral triangle on that page all equal?)

For question 4, you use the same property that you discovered in the last question. The angles of an equilateral triangle always measure 60 degrees. Therefore, you can set up an equation to find the value of x.

Question 5: I think that you should really be able to figure this one out by now, knowing that the two line segments are congruent. If AC is congruent to BC, then the measure of line AC equals the measure of line BC. Using that knowledge, setup an equation to solve for x.

Question 6: Lets call that long line segment, the one that goes from B to C and then continues on, a ray (just for the sake of describing it). Ray BC is a straight line. Knowing this, you know that the sum of the 100 degree angle and angle C has to equal 180 degrees. Therefore, take 180 and subtract 100 degrees to deduce the measure of angle C. Then, use the properties of isosceles triangles, and the fact that the sum of all of the angles in a triangle equals 180 degrees, to determine the measure of the other two angles (hint: is angle C equal in measure to any other angles in the triangle?)

- Oh, I see that other people have already given you all of the answers. Congratulations. You had other people do your homework and didn&#039;t learn a thing! I wish you the best of luck when you exams come up! -

Answer 2

1.a

2.b

3.30

4.b

5.c

6.a

7.a

8.d

This part of geometry is basically algebra with drawings.  If you learn the basic relationships of figures (triangle angles, vertical angles, etc., it becomes fairly straight forward.

Good luck

Answer 3

1...c

2...c

then good luck

and im in algebra 2

Answer 4

A triangle is said to be isosceles if

Two sides in it have equal length, or  

Two angles in it are equal.  

An equilateral triangle is a triangle with all three sides of equal length , corresponding to what could also be known as a &quot;regular&quot; triangle. An equilateral triangle is therefore a special case of an isosceles triangle having not just two, but all three sides equal. An equilateral triangle also has three equal  angles.

1.- ANSWER....A

2.- ANSWER....B

The sum of the angles in a triangle is 180 degrees. An isosceles triangle has two equal angles. if line AB is congruent with Line CA, means that &lt;B and &lt;C are the same.

if &lt;A + &lt;B + &lt;C = 180 and &lt;A = 40

then &lt;B + &lt;C = 180 - 40 = 140

140/2 = 70 ....   &lt;B = 70 and &lt;C = 70

3.- ANSWER:.....D

3B.- Every angle of an equilateral triangle is 60 degrees.

if  Y=(4/3)x + 20   then you know that

(4/3)x + 20 = 60 ---&gt; (4/3)x = 60 - 20 ---&gt; (4/3)x = 40

x = 40/(4/3) ---&gt; x = 30

3b. ANSWER .....A

4.- In an equilateral triangle, every angle is 60 degrees. so if an angle is &quot;x + 10&quot;

x + 10 = 60 ---&gt; x = 60 - 10 ---&gt; x = 50

4.- ANSWER .... B

5.- If AC is congruent with BC means they measure the same

if AC = 6 then BC = 6  then 2x + 2 = 6

2x = 6-2 ---&gt; 2x = 4 ----&gt; x = 4/2 -----&gt; x = 2

5.- ANSWER....... C

6.- If you have an angle of 100 degrees, to complement the angle you need 80 degrees. If &lt; C = 80 then &lt;B = 80 and

&lt;A = 20 degrees

Remember &lt;A + &lt;B + &lt;C = 180

6.- ANSWER......A

7.- x = 4z

     y = 4z

then 4z + 4z + z = 180 degrees

9z = 180 ---&gt; 180/9 ---&gt; z = 20 degrees.

7.-ANSWER....A

8.- Two angles are equal.... so y=70 degrees

8.- ANSWER .... D

Answer 5

1) a

2) b

3) d

4) b

5) c

6) a

7) c

8) d