Lines, Angles and Triangles

The word "geometry" comes from Greek words meaning—

Geometry originated mainly from the need for measuring—

Concepts of geometry were applied to land survey in ancient Egypt approximately how many years ago?

Signs of application of geometry are visible in which civilizations?

Excavations at which sites show evidence of well-planned cities in the Indus Valley civilization?

In the Vedic period, altars (vedis) were constructed maintaining definite—

Vedic altars were usually constituted with—

Which Greek mathematician is credited with the first geometrical proof?

Thales proved logically that a circle is bisected by its—

Pythagoras was a pupil of which mathematician?

About which year did Euclid collect scattered geometrical work into "Elements"?

Euclid's "Elements" was completed in how many chapters?

Euclid's "Elements" is the foundation of—

A solid has how many dimensions?

The three dimensions of a solid are—

The boundary of a solid denotes a—

The six faces of a box represent—

The surface of a sphere is—

A surface has how many dimensions?

Which of the following has only length and breadth and no thickness?

When two surfaces intersect, what is formed?

A line is—

A line has only—

The intersection of two lines produces a—

A point is considered an entity of—

According to Euclid, "A point is that which has—"

According to Euclid, a line has only—

According to Euclid, a surface has—

The edges of a surface are—

"Things which are equal to the same thing, are equal to one another"—is one of Euclid's—

"If equals are added to equals, the wholes are equal"—is an—

"The whole is greater than the part" is an example of an—

"A straight line may be drawn from any one point to any other point" is Euclid's—

According to Euclid's Postulate 2, a terminated line can be—

"A circle can be drawn with any centre and any radius"—is Euclid's—

According to Euclid's Postulate 4, all right angles are—

Euclid's fifth postulate is related to—

Euclid in his "Elements" proved a total of how many propositions?

Statements proved using axioms and postulates are called—

In modern geometry, point, line and plane are taken as—

Admitted properties of point, line and plane are called—

Space is regarded as a set of all—

Plane and straight line are considered—

For two different points, how many straight lines exist on which both points lie?

For three non-collinear points, how many planes exist on which all three points lie?

A straight line passing through two different points on a plane lies—

According to the postulates of plane geometry, space contains—

In each plane, how many straight lines lie?

The points on a straight line correspond to—

Postulates 1 to 5 of plane geometry are collectively called—

The distance between points $P$ and $Q$ is denoted by—

If $P$ and $Q$ are different points, the number $PQ$ is—

$PQ = QP$ shows that distance is—

Postulate 6 (concerning distance) is known as the—

The postulate stating one-to-one correspondence between points on a line and real numbers with $PQ = |a - b|$ is the—

When points on a line are matched to real numbers, the line is called a—

To convert a straight line into a number line, the coordinates of two chosen points are taken as—

Postulate 8 is known as the—

If $P$ corresponds to $a$ on the number line, then $a$ is the—

Which of the following is a method of mathematical proof?

Which philosopher first introduced proof by contradiction?

"A property cannot be accepted and rejected at the same time" is the basis of—

In geometric proof, statements are explained with the help of—

Description of a proposition independent of any figure is called—

Description of a proposition based on a figure is called—

The proper sequence of steps in proving a geometric theorem is— general enunciation → figure & particular enunciation → constructions → ?

A proposition proved directly from the conclusion of a theorem is called a—

Proposals for construction of figures are known as—

Point $C$ is called internal to $A$ and $B$ if $A, C, B$ are different collinear points and—

Three points lying on the same line are called—

The set including $A$, $B$ and all points internal to them is called—

Points strictly between $A$ and $B$ are called—

When two rays in a plane meet at a point, what is formed?

The two rays forming an angle are called the—

The common point of the two rays forming an angle is called the—

The angle formed by two opposite rays at their common end point is a—

The measurement of a straight angle is—

A straight angle equals how many right angles?

Two angles having the same vertex, a common side and lying on opposite sides of the common side are called—

If two adjacent angles formed on a straight line are equal, each is a—

A right angle measures—

The two sides of a right angle are mutually—

An angle less than a right angle is—

An angle greater than one right angle but less than two right angles is—

An angle greater than two right angles and less than four right angles is a—

If the sum of two angles is one right angle, the angles are—

If the sum of two angles is two right angles, the angles are—

The supplement of $130°$ is—

The complement of $35°$ is—

Two angles are opposite (vertical) if the sides of one are the opposite rays of the—

Two intersecting lines produce how many pairs of opposite angles?

The set of points lying on the $Q$-side of $OP$ and the $P$-side of $OQ$ is the ___ region of $\angle POQ$.

The sum of two adjacent angles a ray makes with a straight line at the meeting point equals—

When two straight lines intersect, vertically opposite angles are—

If $\angle AOC = 65°$ at the intersection of $AB$ and $CD$, then $\angle BOD =$

If $\angle AOC = 65°$ at the intersection of $AB$ and $CD$, then $\angle AOD =$

Two angles forming a linear pair are always—

A line cutting two or more lines at distinct points is called a—

A transversal cutting two lines forms how many angles in total?

In the figure where transversal $EF$ cuts $AB$ and $CD$ at $P$ and $Q$, $\angle 1$ and $\angle 5$ are—

Across the same transversal, $\angle 3$ and $\angle 6$ are—

The pair $\angle 4$ and $\angle 6$ are—

The pair $\angle 3$ and $\angle 5$ are—

In a plane, two distinct straight lines having no point in common are—

Two distinct straight lines in a plane have at most how many points in common?

Through a point not on a line, how many lines parallel to it can be drawn?

When a transversal cuts two parallel lines, the corresponding angles are—

When a transversal cuts two parallel lines, the alternate angles are—

When a transversal cuts two parallel lines, the pair of interior angles on the same side are—

If a transversal cuts two lines such that corresponding angles are equal, the lines are—

The perpendicular distance from any point on one of two parallel lines to the other is—

"Lines which are parallel to a given line are parallel to each other"—this is—

$\angle AEF =$ alternate $\angle EFD$ when $AB \parallel CD$ corresponds to which property?

A triangle is a closed figure formed by—

The number of sides in a triangle is—

The number of vertices in a triangle is—

The number of angles in a triangle is—

The sum of the lengths of three sides of a triangle is its—

A line segment from a vertex to the midpoint of the opposite side is called a—

The perpendicular distance from any vertex to the opposite side is the—

By sides, triangles are classified into how many types?

By angles, triangles are classified into how many types?

A triangle with all three sides equal is called—

A triangle with exactly two sides equal is called—

A triangle with all three sides unequal is called—

A triangle with all three angles acute is—

A triangle with one right angle is called—

A triangle having one obtuse angle is called—

When a side of a triangle is produced, the new angle formed is the—

The sum of the three angles of any triangle equals—

The sum of the three interior angles of a triangle in degrees equals—

Each angle of an equilateral triangle measures—

If two angles of a triangle are $50°$ and $70°$, the third angle is—

An exterior angle of a triangle equals the sum of—

An exterior angle of a triangle is greater than each—

The acute angles of a right-angled triangle are—

If one acute angle of a right triangle is $25°$, the other acute angle is—

If one side of an equilateral triangle is produced both ways, the difference between the two exterior angles thus formed is—

In an equilateral $\triangle PQR$ with $QR$ extended to $S$, the interior adjacent angle at $R$ is—

In an equilateral triangle, the exterior angle at any vertex equals—

If two line segments have the same length they are—

If two angles have equal measure they are—

$\triangle ABC \cong \triangle DEF$ implies $AB = DE$, $BC = EF$ and $CA =$

The SAS criterion uses—

The SSS criterion uses—

The ASA criterion uses—

The hypotenuse-side (RHS) criterion applies to—

In a triangle, if two sides are equal, the angles opposite the equal sides are—

In a triangle, if two angles are equal, the sides opposite them are—

The base angles of an isosceles triangle are—

In $\triangle ABC$, if $AB = AC$ and $\angle BAC = 80°$, then $\angle ABC =$

Continuing the previous question, the exterior $\angle ACD$ when $BC$ is produced to $D$ equals—

In a right triangle with legs $3$ and $4$, the hypotenuse is—

In an equilateral triangle, all three medians are—

The triangle formed by joining the midpoints of the sides of an equilateral triangle is—

If one side of a triangle is greater than another, the angle opposite the greater side is—

If one angle of a triangle is greater than another, the side opposite the greater angle is—

The sum of the lengths of any two sides of a triangle is ___ the third side.

The difference of the lengths of any two sides of a triangle is ___ the third side.

Which set of lengths can form a triangle?

Which set CANNOT form a triangle?

The sum of any two exterior angles of a triangle is—

In $\triangle ABC$, $D$ is the midpoint of $BC$. Which inequality holds?

In a triangle, if $AB > AC$ and $AD$ bisects $\angle A$ meeting $BC$ at $D$, then $\angle ADB$ is—

The sum of the three medians of a triangle is ___ the perimeter of the triangle.

The line segment joining the midpoints of two sides of a triangle is parallel to—

The length of this mid-segment is ___ the third side.

In $\triangle ABC$, $D$ and $E$ are midpoints of $AB$ and $AC$. If $BC = 12$, then $DE =$

The mid-segment theorem in this chapter is proved using which congruence criterion?

In a right triangle with the right angle at $B$, if $D$ is the midpoint of hypotenuse $AC$, then $BD =$

In a right-angled triangle, the square on the hypotenuse equals—

If the legs of a right triangle are $6$ and $8$, the hypotenuse is—

If the hypotenuse is $13$ and one leg is $5$, the other leg is—

Which triple is Pythagorean?

In $\triangle ABC$, $\angle ABC = 1$ right angle. If $AB = 9$ and $BC = 12$, then $AC =$

In Example 1, $AB = AC$ and $BA$ is produced to $D$ such that $AD = AC$. Then $\angle BCD$ equals—

In Example 1, the inequality proved is $BC + CD >$

In Example 2, the three medians of $\triangle PQR$ meet at the point—

Example 2 proves that $PA + QB + RC <$

Any point on the perpendicular bisector of a line segment is—

In an isosceles triangle, the bisector of the vertical angle—

If $\angle C$ and $\angle D$ are supplementary and $\angle C - \angle D = 60°$, then $\angle C =$