It seems deceivingly simple...but I'll ask just in case...
Given: line j is perpendicular to line k, forming a linear pair of angles, angle 1 and 2.
Prove: angle 1=angle 2
2006-10-25 12:34:52 · 6 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
Perpendicular lines meet at right angles.
Right angles have measures of 90 degrees.
90 = 90
So angle 1 = angle 2.
2006-10-25 12:38:43 · answer #1 · answered by Puzzling 7 · 1⤊ 0⤋
Line j is perpendicular to line A. It means that it forms four angles each of 90 degrees on either side of line j and k. Any one of these can be angle 1 or angle 2. Ange 1 is always equal to angle 2.
2006-10-26 08:01:07 · answer #2 · answered by Akilesh - Internet Undertaker 7 · 0⤊ 0⤋
Line j is perpendicular to line k ; given
angle 1 and angle 2 are right angles ; def. of per. lines
angle 1 and angle 2 = 90 degrees ; def. of right angles
angle 1 = angle 2 ; def. of equality
2006-10-25 19:55:59 · answer #3 · answered by black_star_47001 3 · 0⤊ 0⤋
Perpendicular lines Intersect like a + sign.
A circle has 360° no?
divide that by 4 parts and u get 90°.
So even with angles 1,2,3, and 4, they are all congruent or equal. Really simple.
2006-10-25 19:43:33 · answer #4 · answered by soccerdude 2 · 0⤊ 0⤋
To have perpendicular lines, means you have at least two 90 Degree angles, which equal one another.
2006-10-25 19:43:30 · answer #5 · answered by Asterisk_Love♥ 4 · 0⤊ 0⤋
Perpendicular Bisector, line j is perpendicular to line k, using the three Euclidean rules
Segments AC, BC and AB are congruent to each other, since they are all radii of circle A and circle B. Also, since segments AC, BC and AB are congruent to each other, triangle ABC is equilateral. Therefore, each angle measures 60 degrees, angle A, angle B, and angle C. Since line CE bisects angle ACB, angle ECB measures 30 degrees. We know angle EBC measures 60 degrees, ECB measures 30 degrees, thus, angle CEB must measure 90 degrees. Therefore, by definition of perpendicular lines, line j is perpendicular to line k.
Following on the same argument above for the midpoint, we know that triangle ACE is congruent to triangle BCE (see above). Therefore, by corresponding parts of congruent triangles, angle AEC is congruent to angle BEC. Since angle AEC and angle BEC form a linear pair and the angles are congruent to one another, it follows that angle AEC and angle BEC measure 90 degrees. Therefore, by definition of perpendicular, line AB is perpendicular to line EC.
2006-10-25 19:47:42 · answer #6 · answered by Jamil Ahmad G 3 · 0⤊ 0⤋