If two parallel lines are cut by a transversal, then which of the following is true?
Alternate interior angles are congruent.
When a transversal cuts two parallel lines, it forms pairs of alternate interior angles that lie on opposite sides of the transversal, between the two lines.
By the parallel-lines property, each pair of alternate interior angles is equal, i.e. the angles are congruent.
Since they are equal, their difference is 0°, not 60°; they are not always complementary (sum 90°) or supplementary (sum 180°) — it is the co-interior angles on the same side that are supplementary.
Hence, the answer is: Alternate interior angles are congruent.
Similar Questions
In a rectangle, one diagonal is inclined to one of its sides at 35°. Find the measure of the acute angle between its two diagonals.
The sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 84 cm. What is the area of the triangle?
What is the measure of each interior angle of a regular 96-gon?
AB is parallel to CD. A transversal PQ intersects AB and CD at E and F, respectively, and ∠PEB = 75°. G is a point between AB and CD such that ∠BEG = 45° and ∠GFE = 19°. What is the measure of ∠EGF?
In a trapezium PQRS, PQ∥RS. Calculate ∠R if ∠P = 72° and ∠Q = 54°.
The sides of a triangle are in the ratio 13 : 14 : 15 and its perimeter is 42 cm. What is the area of the triangle?
In a quadrilateral PQRS, ∠P = \((4x + 8)^\circ\), ∠Q = \((3x + 2)^\circ\), ∠R = \(75^\circ\) and ∠S = \((x - 5)^\circ\). The shortest angle of the quadrilateral is
A trapezium has parallel sides 18 cm and 12 cm. The height of the trapezium is equal to the average of the lengths of the two parallel sides. What is the area of the trapezium?
The area of a square field is 6561 m2. Its perimeter (in m) is:
Important Questions from Plane Figures
If the area of a square is 625 cm 2, then what is the perimeter of the square?
The area and the perimeter of a sheet of paper are 240 cm 2and 68 cm, respectively. What would be its length and breadth?
One side of rectangular field is 15 meters and one of its diagonals is 17 meters. Then find the area of the field.
The perimeter and the length of one of the diagonals of a rhombus is 26 cm and 5 cm respectively. Find the length of its other diagonal (in cm).
ABCD is a trapezium in which AB is parallel to DC. Let E and F be the midpoints on AD and BC respectively. If EF = 10 cm and AB - DC = 4 cm, then what is the value of AB × DC?
