Advertisements
Advertisements
Question
In the given figure, ∠CAB = 90° and AD⊥BC. Show that ΔBDA ~ ΔBAC. If AC = 75cm, AB = 1m and BC = 1.25m, find AD.
Solution
In Δ BDA and Δ BAC, we have :
∠𝐵𝐷𝐴= ∠𝐵𝐴𝐶=90°
∠𝐷𝐵𝐴= ∠𝐶𝐵𝐴 (𝐶𝑜𝑚𝑚𝑜𝑛)
Therefore, by AA similarity theorem, Δ BDA - Δ BAC
⇒ `(AD)/(AC)=(AB)/(BC)`
`⇒(AD)/0.75=1/1.25`
`⇒ AD=0.75/1.25`
= 0.6 m or 60 cm
APPEARS IN
RELATED QUESTIONS
Examine each pair of triangles in Figure, and state which pair of triangles are similar. Also, state the similarity criterion used by you for answering the question and write the similarity relation in symbolic form
figure (i)
figure 2
figure 3
figure 4
figure 5
figure 6
figure 7
In the given figure, two chords AB and CD of a circle intersect each other at the point P (when produced) outside the circle. Prove that
(i) ΔPAC ∼ ΔPDB
(ii) PA.PB = PC.PD
Prove that, in a right triangle, the square on the hypotenuse is equal to the sum of the squares on the other two sides.
In the given figure, AB || EF || DC; AB = 67.5 cm, DC = 40.5 cm and AE = 52.5 cm.
- Name the three pairs of similar triangles.
- Find the lengths of EC and EF.
The ratio between the corresponding sides of two similar triangles is 2 is to 5. Find the ratio between the areas of these triangles.
ABC is a triangle. PQ is a line segment intersecting AB in P and AC in Q such that PQ || BC and divides triangle ABC into two parts equal in area. Find the value of ratio BP : AB.
The given diagram shows two isosceles triangles which are similar. In the given diagram, PQ and BC are not parallel; PC = 4, AQ = 3, QB = 12, BC = 15 and AP = PQ.
Calculate:
- the length of AP,
- the ratio of the areas of triangle APQ and triangle ABC.
ΔABC~ΔPQR and ar(ΔABC) = 4, ar(ΔPQR) . If BC = 12cm, find QR.
The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas.
Δ ABC ~ Δ DEF. If BC = 3cm , EF=4cm and area of Δ ABC = 54 cm2 , find area of Δ DEF.
In figure , DEF is a right -angled triangle with ∠ E = 90 °.FE is produced to G and GH is drawn perpendicular to DE = 8 cm , DH = 8 cm ,DH = 6 cm and HF = 4 cm , find `("Ar" triangle "DEF")/("Ar" triangle "GHF")`
In the figure , ABCD is a quadrilateral . F is a point on AD such that AF = 2.1 cm and FD = 4.9 cm . E and G are points on AC and AB respectively such that EF || CD and GE || BC . Find `("Ar" triangle "BCD")/("Ar" triangle "GEF")`
AD and BC are two straight lines intersecting at 0. CD and BA are perpendirulars from Band Con AD. If AB=6cm, CD =9cm, AD =20cm and BC=25cm, find the lengths of AO, BO, CO and DO.
A triangle ABC has been enlarged by scale factor m = 2.5 to the triangle A' B' C'. Calculate : the length of C' A' if CA = 4 cm.
If ΔABC, D and E are points on AB and AC. Show that DE || BC for each of the following case or not:
AB = 10.8cm, BD = 4.5cm, AC = 4.8cm, and AE = 2.8cm
In ΔABC, point D divides AB in the ratio 5:7, Find: DE, If BC = 4.8cm
Prove that the external bisector of an angle of a triangle divides the opposite side externally n the ratio of the sides containing the angle.
In the figure, AB || RQ and BC || SQ, prove that `"PC"/"PS" = "PA"/"PR"`.
In a right-angled triangle ABC, ∠B = 90°, P and Q are the points on the sides AB and AC such as PQBC, AB = 8 cm, AQ = 6 cm and PA:AB = 1:3. Find the lengths of AC and BC.
ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm
Check whether the triangles are similar and find the value of x
If figure OPRQ is a square and ∠MLN = 90°. Prove that QR2 = MQ × RN
Construct a triangle similar to a given triangle PQR with its sides equal to `2/3` of the corresponding sides of the triangle PQR (scale factor `2/3 < 1`)
The perimeters of two similar triangles ∆ABC and ∆PQR are 36 cm and 24 cm respectively. If PQ = 10 cm, then the length of AB is
Which of the following is not a test of similarity?
In fig. BP ⊥ AC, CQ ⊥ AB, A−P−C, and A−Q−B then show that ΔAPB and ΔAQC are similar.
In ΔAPB and ΔAQC
∠APB = [ ]° ......(i)
∠AQC = [ ]° ......(ii)
∠APB ≅ ∠AQC .....[From (i) and (ii)]
∠PAB ≅ ∠QAC .....[______]
ΔAPB ~ ΔAQC .....[______]
Side of equilateral triangle PQR is 8 cm then find the area of triangle whose side is half of the side of triangle PQR.
ΔABC and ΔBDE are two equilateral triangles such that D is the mid point of BC. Ratio of the areas of triangle ΔABC and ΔBDE is ______.
In ∠BAC = 90° and AD ⊥ BC. A then ______.
If ∆ABC ~ ∆QRP, `(ar(ABC))/(ar(PQR)) = 9/4`, AB = 18 cm and BC = 15 cm, then PR is equal to ______.
