Construction of Triangles - Class VIII
Practice problems on constructing triangles using various methods: when given perimeter and base angles, SAS conditions, and constructing similar triangles with scale factor
Questions
Construct a triangle $PQR$, whose perimeter is $22 cm$ and whose sides are in the ratio $2 : 4 : 5$. Measure the sides of the triangle.
- $5, 7, 10$
- $4, 8, 10$
- $5, 8, 9$
- None of these
Construct a $\triangle ABC$ in which $AB= 5.4\ cm, \angle CAB= 45^{\circ}$ and $AC + BC= 9\ cm.$Then, $m\angle ACB$ is:
- $55^o$
- $75^o$
- $85^o$
- None of these
For constructing a triangle whose perimeter and both base angles are given, the base length is equal to:
- the length of the perimeter
- the length of the largest side
- the difference between the largest and the shortest side
- None of these
Choose the correct statement:
- Of all the line segments that can be drawn from a point outside a line, the perpendicular is the shortest.
- The difference of two sides of a triangle is equal to the third side.
- The sum of the three sides of a triangle is less than the sum of its three medians.
- If two sides of a triangle are unequal then the larger side has the smaller angle opposite to it.
For constructing a triangle when the base, one base angle and the difference between lengths of other two sides are given, the base length is equals to:
- The difference between lengths of other two sides
- The given base length
- The largest side
- None of these
The construction of a $\Delta ABC$ in which $BC=6$ $cm$ and $\angle B=50^\circ$, is not possible when $(AB-AC)$ is equal to:
- $5.6\ cm$
- $5\ cm$
- $6\ cm$
- $4.8\ cm$
The construction of $\Delta EFG$ when $FG=3$ $cm$ and m$\angle G=60^\circ$ is possible when difference of $EF$ and $EG$ is equal to:
- $3.2$ $cm$
- $3.1$ $cm$
- $3$ $cm$
- $2.8$ $cm$
For constructing a triangle whose perimeter and both base angles are given, the first step is to:
- Draw a base of any length
- Draw the base of length $=$ perimeter
- Draw the base angles from a random line.
- Draw a base of length $=\dfrac13 \times$ perimeter.
The construction of $\triangle ABC$ in which $AB = 6\ cm, \angle A = 30^\circ$, is not possible when $AC+BC = $
- $6.3\ cm$
- $7.2\ cm$
- $5.6\ cm$
- $6.9\ cm$
The construction of $\triangle ABC$ in which $AB = 5\ cm, \angle A = 45^\circ$, is possible when $AC+BC = $
- $4.8\ cm$
- $5.6\ cm$
- $3.2\ cm$
- $2.8\ cm$
Construct a $\triangle ABC$ in which:
$AB= 5.4\ cm$, $\angle CAB= 45^{0}$ and $AC, +, BC= 9\ cm$. Then the length of $AC$ (in $cm.$) is:
- $4$
- $7$
- $5$
- None of these
The construction of $\Delta LMN$ when $MN=7$ $cm$ and $m\angle M=45^\circ$ is not possible when difference of $LM$ and $LN$ is equal to:
- $4.5$
- $5.5$
- $6.5$
- $7.5$
Which of the following could be the value of $AC-BC$ in the construction of a triangle $ABC$ in which base $AB = 5 cm, \angle A = 30^{\circ}$?
- $5.5$
- $5$
- $2.5$
- None of these
The construction of $\Delta LMN$ when $MN=6$ $cm$ and $m\angle M=45^\circ$ is not possible when difference between $LM$ and $LN$ is equal to:
- $6.9$ $cm$
- $5.2$ $cm$
- $5$ $cm$
- $4$ $cm$
To construct a triangle similar to a given triangle ABC with its sides 6/5th of the corresponding sides of $\Delta$ABC. Correct order of steps of construction -
(a) Draw a ray AX inclined at certain angle with AB on opposite side of C.
(b) Starting from A, cut off six equal line segments AX$ _1$, X$ _1$X$ _2$, X$ _2$X$ _3$, X$ _3$X$ _4$, X$ _4$X$ _5$ and X$ _5$X$ _6$ on AX.
(c) Draw a line B'C' parallel to BC to intersect AC produced at C'
(d) Join X$ _5$B and draw a line X6B' parallel to X5B, to intersect AB produced at B'.
- abcd
- acbd
- abdc
- adcb
Construct a $\Delta ABC$, whose perimeter is $10.5 cm$ and base angles are $60^o$ and $45^o$. Find the third angle.
- $75^o$
- $45^o$
- $90^o$
- $60^o$