Practical Geometry

In practical geometric constructions, which instruments are used?

In which situation is high precision of geometrical drawing required?

In previous classes students learnt how to construct which figures using ruler and compasses?

The focus of Chapter 7 (Practical Geometry) is the construction of—

To construct a unique triangle, how many independent parts of the triangle must be specified?

The sum of the three angles of a triangle equals—

If three angles only are specified, the number of triangles that can be drawn is—

Which of the following is NOT one of the listed data combinations that determines a unique triangle in class seven?

"Hypotenuse and a side" determines a unique triangle when the triangle is—

Which combination represents the SAS condition?

Which combination represents the ASA condition?

The combination "two angles and an opposite side" corresponds to—

Triangles with the same angles but different sizes are called—

In Construction 1 the given data are—

From ray $BE$, the line segment $BC$ is cut equal to—

The line segment $BD$ from ray $BF$ is cut equal to—

At $C$, the angle $\angle DCG$ is constructed equal to—

In $\triangle ACD$, since $\angle ADC = \angle ACD$, it follows that—

In the constructed triangle $\triangle ABC$, $BA + AC$ equals—

In the alternate method of Construction 1, line segment $CD$ is bisected by—

In $\triangle ACR$ and $\triangle ADR$, the included angle $\angle ARC = \angle ARD$ equals—

The congruence $\triangle ACR \cong \triangle ADR$ is established by—

After joining $A$ and $C$ in the alternate method, $AC$ equals—

In Construction 2 the difference $d$ is cut on ray $BF$ as line segment—

The angle constructed at $C$ in Construction 2 equals—

In the resulting triangle $\triangle ABC$, the difference $AB - AC$ equals—

If the given base-adjacent angle is NOT acute, Construction 2 is—

In Construction 2, $AC = AD$ because in $\triangle ACD$—

Construction 2 essentially differs from Construction 1 in that—

In Construction 3, on ray $DF$ the part $DE$ is cut equal to—

At points $D$ and $E$ the angles $\angle EDL$ and $\angle DEM$ are made equal respectively to—

The rays $DG$ and $EH$ are—

At the point $A$ where the bisectors meet, $\angle DAB$ is constructed equal to—

In $\triangle ABD$, $AB = DB$ because—

In $\triangle ACE$, $CA = CE$ because—

The perimeter $AB + BC + CA$ in the constructed triangle equals—

In Construction 3, $\angle ABC$ equals—

In Example 1, $PQ$ is drawn equal to—

The angle $\angle QPL$ at $P$ is—

The angle $\angle PQM$ at $Q$ is—

The bisectors $PG$ and $QH$ of the two angles intersect at—

After drawing perpendicular bisectors of $PA$ and $QA$, they meet $PQ$ at—

The base $AB$ is cut equal to—

The angle $\angle XAE$ at $A$ measures—

The line segment $AD$ is taken equal to—

At $B$, $\angle DBC$ is constructed equal to—

The perimeter of the square in part (3) of Example 2 equals—

With perimeter $2s$ and $s = 6$ cm, the side of the square equals—

In the square construction, $AE$ is drawn at $A$ such that—

In the square $ABCD$, the angle $\angle BAD$ equals—

Number of independent data required to construct a definite quadrilateral is—

With only four sides given, a definite quadrilateral can be constructed?

Which of the following is NOT a listed combination that determines a quadrilateral uniquely?

A diagonal of a quadrilateral divides it into—

When one or two diagonals are given, the construction of a quadrilateral is usually done by—

In Construction 4, line segment $AC$ is cut equal to—

The point $O$ is the—

At $O$ the angle $\angle AOP$ is constructed equal to—

From $OP$ and $OQ$, segments $OB$ and $OD$ are cut each equal to—

In $\triangle AOB$ and $\triangle COD$, $OA = OC$ equals—

The congruence $\triangle AOB \cong \triangle COD$ uses—

From $\angle ABO = \angle CDO$ being alternate angles, it follows that—

In Construction 4, the included angle between the diagonals is—

In Construction 5, on ray $AX$ the segment $AB$ is cut equal to—

The arcs at $A$ and $B$ are drawn with radii respectively—

The point of intersection of these arcs gives—

To complete the parallelogram, $OC$ is cut from $OE$ equal to—

In Construction 5, $\triangle AOB \cong \triangle COD$ is justified by—

In Example 3 the parallel sides satisfy—

From ray $AX$, the line segment $AB$ is cut equal to—

From line segment $AB$, $AE$ is cut equal to—

The line through $E$ parallel to $AY$ meets ray $BZ$ at—

The segment $CD$ is drawn—

Quadrilateral $AECD$ in Example 3 is a—

The line segment $RQ$ is cut equal to—

At $R$, the angle constructed equals—

At $Q$, the angle constructed equals—

In Example 4, the rhombus to be constructed has each side equal to—

The angle of the rhombus in Example 4 equals—

To complete the rhombus, after marking $BA$ and $BC$ equal, equal arcs are drawn from $A$ and $C$ to meet at—

A parallelogram can be uniquely constructed when only the following are given—

A square can be uniquely constructed when only the following is given—

The four sides of a square are—

An angle of a square is always—

A rhombus can be constructed when its perimeter and one angle are given because—

Given three sides $3$ cm, $3.5$ cm, $2.8$ cm, a triangle can be constructed because—

With two sides $4$ cm and $3$ cm and included angle $60^\circ$, the construction uses—

With two angles $60^\circ$, $45^\circ$ and their adjacent side $5$ cm, the construction uses—

With two angles $60^\circ$, $45^\circ$ and the side opposite the $45^\circ$ angle equal to $5$ cm, the construction uses—

With hypotenuse $6$ cm and a side $4$ cm of a right-angled triangle, the third side equals—

Base $3.5$ cm, base-adjacent angle $60^\circ$, sum of other two sides $8$ cm — which construction applies?

Base $5$ cm, base-adjacent angle $45^\circ$, difference of other two sides $1$ cm — which construction applies?

Base-adjacent angles $60^\circ$, $45^\circ$ and perimeter $12$ cm — which construction applies?

Constructing an equilateral triangle whose perimeter is given requires that each side equal—

For a right-angled triangle with hypotenuse and the sum of the other two sides given, the construction is similar in spirit to—

The base, an obtuse base-adjacent angle and the difference of the other two sides — this case is the obtuse-angle analogue of—

The two angles of a right-angled triangle that allow constructing it must sum to—

From the options $60^\circ$ & $36^\circ$, $40^\circ$ & $50^\circ$, $30^\circ$ & $70^\circ$, $80^\circ$ & $20^\circ$, the valid pair of two acute angles of a right-angled triangle is—

If two sides of a triangle are $4$ cm and $9$ cm, the third side $x$ must satisfy—

From the options $4$, $5$, $6$, $13$, the only valid third side of the triangle in Q99 is—

A unique quadrilateral can be constructed if there is given—

Constructing a quadrilateral with four sides $3$ cm, $3.5$ cm, $2.5$ cm, $3$ cm and one angle $45^\circ$ uses the data combination—

Quadrilateral with sides $3.5$, $4$, $2.5$, $3.5$ cm and a diagonal $5$ cm uses the data combination—

Quadrilateral with three sides $3.2$, $3$, $3.5$ cm and two diagonals $2.8$, $4.5$ cm uses—

Quadrilateral with three sides $3$, $3.5$, $4$ cm and two angles $60^\circ$, $135^\circ$ uses—

A parallelogram with diagonals $4$ cm, $6.5$ cm and included angle $45^\circ$ corresponds to—

A parallelogram with one side $4$ cm and diagonals $5$ cm, $6.5$ cm corresponds to—

For quadrilateral $ABCD$ with sides $AB$, $BC$ and angles $\angle B$, $\angle C$, $\angle D$ given, the data count is—

Quadrilateral $ABCD$ with diagonal segments $OA = 4$, $OB = 5$, $OC = 3.5$, $OD = 4.5$ cm and $\angle AOB = 80^\circ$ uses how many data?

To construct a rhombus given side $3.5$ cm and one angle $45^\circ$, the additional implicit data come from—

To construct a rhombus given a side and a diagonal, the additional implicit data come from—

A rhombus can be uniquely constructed if only its two diagonals are given because—

A square's perimeter alone is enough to construct it because the side equals—

In a right-angled triangle with hypotenuse $5$ cm and a side $4$ cm, the other side equals—

The perimeter of the triangle in Q114 equals—

The side of a square whose perimeter equals the perimeter of the triangle in Q114 is—

In quadrilateral $ABCD$ with $\angle A = 85^\circ$, $\angle B = 80^\circ$, $\angle C = 95^\circ$, the angle $\angle D$ equals—

To construct a parallelogram with two adjacent sides $AB = 4$ cm, $BC = 5$ cm and included $\angle B = 80^\circ$, the minimum number of independent data needed is—

The two equal sides of an isosceles right-angled triangle are $18$ cm. The area of the triangle equals—

In a rhombus, which of the following are correct: (i) four sides are mutually equal, (ii) opposite angles are equal, (iii) the two diagonals bisect each other at right angles?

In a rectangle $ABCD$ the diagonals intersect at $E$, and $F$ is on $BC$ with $BF = 2$ cm and $EF = 3$ cm. The length of diagonal $BD$ equals—

With the data of Q121, the area of rectangle $ABCD$ equals—