In an isosceles $\triangle\text{ABC},$ if $AC = BC$ and $AB^2 = 2AC^2$ then $\angle\text{C}=?$
- A$30^\circ$
- B$45^\circ$
- C$60^\circ$
- ✓$90^\circ$
Answer: D.
View full solution →Question types
Triangles question types
202 questions across 5 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
202
Questions
5
Question groups
5
Question types
01
M.C.Q (1 Marks)
58 Q→022 Marks Questions
16 Q→033 Marks Question
52 Q→044 Marks Questions
70 Q→055 Marks Question
6 Q→Sample Questions
Triangles questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In an equilateral triangle ABC, if $\text{AD}\perp\text{BC}$ then which of the following is true?
- A$2AB^2 = 3AD^2$
- B$4AB^2 = 3AD^2$
- ✓$3AB^2 = 4AD^2$
- D$3AB^2 = 2AD^2$
Answer: C.
View full solution →In $\triangle\text{ABC},\text{DE }||\text{ BC}$ such that $\frac{\text{AD}}{\text{DB}}=\frac{3}{5}. AC = 5.6\ cm$ then $AE =?$
- A$4.2\ cm$
- B$3.1\ cm$
- C$2.8\ cm$
- ✓$2.1\ cm$
Answer: D.
View full solution →In a $\triangle\text{ABC},$ it is given that $AD$ is the internal bisector of $\angle\text{A}.$ If $AB = 10\ cm, AC = 14\ cm$ and $BC = 6\ cm,$ then $CD = ?$
- A$4.8\ cm$
- ✓$3.5\ cm$
- C$7\ cm$
- D$10.5\ cm$
Answer: B.
View full solution →In a $\triangle\text{ABC},$ if $DE$ is drawn parallel to $BC,$ cutting $AB$ and $AC$ at $D$ and $E$ respectively such that $AB = 7.2\ cm, AC = 6.4\ cm$ and $AD = 4.5\ cm.$ Then, $AE =?$
- A$5.4\ cm$
- ✓$4\ cm$
- C$3.6\ cm$
- D$3.2\ cm$
Answer: B.
View full solution →$\triangle\text{ABC}\sim\triangle\text{DEF}$ and their areas are respectively $64\ cm^2$ and $121\ cm^2$. If $EF = 15.4\ cm$, find $BC$.
View full solution →$ABC$ is an isosceles triangle, right-angled at $B$. Similar triangle $ACD$ and $ABE$ are constructed on sides $AC$ and $AB$. Find the ratio between the areas of $\triangle\text{ABE}$ and $\triangle\text{ACD}.$
View full solution →$\triangle\text{ABC}$ and $\triangle\text{DBC}$ lie on the same side of BC, as shown in the figure. From a point P on BC, PQ || AB and PR || BD are drawn, meeting AC at Q and CD at R respectively. Prove that QR || AD.
View full solution →In a $\triangle\text{ABC},\text{AD}$ is a median and $\text{AL}\perp\text{BC}.$
Prove that:
View full solution →Prove that:
- $\text{AC}^2=\text{AD}^2+\text{BC}.\text{DL}+\Big(\frac{\text{BC}}{2}\Big)^2$
- $\text{AB}^2=\text{AD}^2-\text{BC}.\text{DL}+\Big(\frac{\text{BC}}{2}\Big)^2$
- $\text{AC}^2+\text{AB}^2=2\text{AD}^2+\frac{\text{1}}{2}\text{BC}^2$
The areas of two similar triangles ABC and PQR are in the ratio 9 : 16. If BC = 4.5cm, find the length of QR.
Prove that the ratio of the perimeters of two similar triangles is the same as the ratio of their corresponding sides.
The corresponding altitudes of two similar triangles are 6cm and 9cm respectively, Find the ratio of their areas.
In $\triangle\text{ABC},\text{AB}=\text{AC}.$ Side BC is produced to D. prove that
$(\text{AD}^2-\text{AC}^2)=\text{BD}.\text{CD}$
View full solution →$(\text{AD}^2-\text{AC}^2)=\text{BD}.\text{CD}$
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}$ such that DE || BC:
AD = (7x - 4)cm, AE = (5x - 2)cm, DB = (3x + 4)cm and EC = 3x cm.
View full solution →AD = (7x - 4)cm, AE = (5x - 2)cm, DB = (3x + 4)cm and EC = 3x cm.
D and E are points on the sides AB and AC respectively of a $\triangle\text{ABC}.$ In the following cases, determine whether DE || BC or not. AD = 7.2cm, AE = 6.4cm, AB = 12cm and AC = 10cm.
View full solution →In the given figure, if $\angle\text{ADE}=\angle\text{B},$ show that $\triangle\text{ADE}\sim\triangle\text{ABC}.$ If AD = 3.8cm, AE = 3.6cm, BE = 2.1cm and BC = 4.2cm, find DE.
View full solution →State the AAA-similarity criterion.
$\triangle\text{ABC}$ is right-angled at A and $\text{AD}\perp\text{BC}.$ If BC = 13cm and AC =5cm, find the ratio of the areas of $\triangle\text{ABC}$ and $$$\triangle\text{ADC}.$
View full solution →A ladder is placed in such a way that its foot is at a distance of 15m from a wall and its top reaches a window 20m above the ground. Find the length of the ladder.
For the following statments state whether true (T) or false(F):
Two circles with different radii are similar.
Two circles with different radii are similar.
Find the length of each side of a rhombus whose diagonals are 24cm and 10cm long.
State the SSS-criterion for similarity of trianglrs.
If $\triangle\text{ABC}\sim\triangle\text{DEF}$ such that 2AB = DE and BC = 6cm, find EF.
View full solution →For the following statments state whether true (T) or false(F):
In a $\triangle\text{ABC},\text{AB}=6\text{cm},\angle\text{A}=45^\circ$ and $\text{AC}=8\text{cm}$ and in a $\triangle\text{DEF},\text{DF}=9\text{cm},\angle\text{D}=45^\circ$and $\text{DE}=12\text{cm},$ then $\triangle\text{ABC}\sim\triangle\text{DEF}.$
View full solution →In a $\triangle\text{ABC},\text{AB}=6\text{cm},\angle\text{A}=45^\circ$ and $\text{AC}=8\text{cm}$ and in a $\triangle\text{DEF},\text{DF}=9\text{cm},\angle\text{D}=45^\circ$and $\text{DE}=12\text{cm},$ then $\triangle\text{ABC}\sim\triangle\text{DEF}.$
In the given figure, D is the midpoint of side BC and $\text{AE}\perp\text{BC}.$ If BC = a, AC = b, AB = c, ED = x, AD = p and AE = h, prove that.
$\text{b}^2=\text{p}^2+\text{ax}+\frac{\text{a}^2}{4}$
View full solution →$\text{b}^2=\text{p}^2+\text{ax}+\frac{\text{a}^2}{4}$
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