In an isosceles Itriangleitext ${A B C},$ if $A C=B C$ and $A B^2=2 A C^2$ then langleltext ${C}=?$
- A$30^{\circ}$
- B$45^{\circ}$
- C$60^{\circ}$
- ✓$90^{\circ}$
Answer: D.
View full solution →Question types
Triangles question types
202 questions across 4 question groups — pick any mix to generate a Maths paper with step-by-step answer keys.
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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 $\text{ABC}$, if $\text{AD}\perp\text{BC}$ then which of the following is true?
- A$2 A B^2=3 A D^2$
- B$4 A B^2=3 A D^2$
- ✓$3 A B^2=4 A D^2$
- D$3AB^2=2 A D^2$
Answer: C.
View full solution →In $\triangle\text{ABC},\text{DE }||\text{ BC}$ such that $\frac{\text{AD}}{\text{DB}}=\frac{3}{5}.$ AC = 5.6cm then AE =?
- A4.2cm
- B3.1cm
- C2.8cm
- ✓2.1cm
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 = 10cm, AC = 14cm and BC = 6cm, then CD = ?
- A4.8cm
- ✓3.5cm
- C7cm
- D10.5cm
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 = 7.2cm, AC = 6.4cm and AD = 4.5cm. Then, AE =?
- A5.4cm
- ✓4cm
- C3.6cm
- D3.2cm
Answer: B.
View full solution →$\triangle\text{ABC}\sim\triangle\text{DEF}$ and their areas are respectively $64cm^2 and 121cm^2$. If $EF = 15.4cm$, 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.
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