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From Wikipedia
In geometry, a transversal line is aline that passes through two or more other coplanar lines at different points.
In Euclidean geometry if lines a and b are parallel, and line t intersects lines a and b, then corresponding angles formed by line t and the parallel lines are congruent.
thumbright300pxAlternate exterior angles created by a transversal of two lines. thumbright300pxAlternate interior angles created by a transversal of two lines.
Alternate angles
A transversal line is a line that transverses other lines
Theorems
There are at least eight geometrical theorems concerning transversals. They are as follows:
Theorem 9 If a transversal intersects two parallel lines, then the alternate interior angles are congruent.
Theorem 10 If a transversal intersects two parallel lines, then the corresponding angles are congruent.
Theorem 11 If a transversal intersects two parallel lines, then the alternate exterior angles are congruent.
Theorem 12 If a transversal intersects two parallel lines, then the interior angles on the same side of the transversal are supplementary.
The next four theorems are converses of the previous four theorems.
Theorem 13 If a transversal intersects two lines so that alternate interior angles are congruent, then the lines are parallel.
Theorem 14 If a transversal intersects two lines so that corresponding angles are congruent, then the lines are parallel.
Theorem 15 If a transversal intersects two lines so that alternate exterior angles are congruent, then the lines are parallel.
Theorem 16 If a transversal intersects two lines so that interior angles on the same side of the transversal are supplementary, then the lines are parallel.
Proofs
Theorem 9
Given: y ll z; transversal t intersects line y and z at A and B; O is the midpoint of lineSEGMENTAB.
Prove: angle 1 is congruent to angle 3; angle 2 is congruent to angle 4.
1. y ll z; transversal intersects lines y and z at A and B; O is the midpoint of line AB.
2. Through O, draw line CD perpendicular to z.(P. means Postulate)
3. Line CD is perpendicular to y.(T. means Theorem)
4. Angle ACO and BDO are right angles.
5. Î”ACO and BDO are right triangles.
6. Angle 5 is congruent to angle 6.
7. Line AO is congruent to line BO.
8. âˆ´ Î”ACO is congruent to Î”BDO.
9. âˆ´ Angle 1 is congruent to angle 3.
10. Angle 2 is supplementary to angle 1; angle 4 is supplementary to angle 3.
11. âˆ´ Angle 2 is congruent to angle 4.
Theorem 11
thumbcenter500pxTheorem 11 Formal Proof Image.Given: Transversal t intersects lines m and n; m ll n.
Prove: Angle 1 is congruent to angle 7.
1. Transversal t intersects lines m and n; m ll n.
2. Angle 3 is congruent to angle 5.
3. Angle 1 is congruent to angle 3; angle 5 is congruent to angle 7.
4. âˆ´ Angle 1 is congruent to angle 7.
Theorem 12
Given: Transversal t intersects lines m' and n; m ll n.
Prove: Angle 1 is supplementary to angle 2.
1. Transversal t intersects lines m and n ; m ll n.
2. Angle 2 is congruent to angle 3.
3. Angle 1 is supplementary to angle '3.
4. âˆ´ Angle 1 is supplementary to angle 2.
In geometry and trigonometry, a acute angle is an angle that bisects the angle formed by ten halves of a straight line. More precisely, if a line is placed so that its endpoint is on a ray and the adjacent angles are equal, then they are right angles. As a rotation, a right angle corresponds
From Yahoo Answers
Answers:ok. well supplementary means that the sum of two angles equals 180 degrees. as compared to complementary, which means that the sum of two angles equals 90 degrees. adjacent angles are angles right next to each other. in the diagram, angle A and angle B are supplementary adjacent angles. i can't put a picture here, but ill let you design your own diagram. first, draw a big X. in the top part of the X, put an A. then, put a B in the right side of the X. the two angles you just labeled are supplementary adjacent angles. i know this is kinda dumb, but it makes the most sense to me to do it this way. :D
Answers:maximum two acute angles. only eight non straight angles maximum, minimum zero when third line is perpendicular to parallel lines.
Answers:Vertical angles When two lines intersect, four angles are formed. The nonadjacent pairs are called vertical angles, not because they are "up and down", but because they share a vertex.
Answers:A = Vertically opposite angles, B= Adjacent angles C=Supplementary angles D=Complementary Angles