Advertisements
Advertisements
Question
In ∆ABC, AP ⊥ BC, BQ ⊥ AC B– P–C, A–Q – C then prove that, ∆CPA ~ ∆CQB. If AP = 7, BQ = 8, BC = 12 then Find AC.
Solution
n ∆CPA and ∆CQB,
∠CPA ≅ ∠CQB [Each angle is of measure 90°]
∠ACP ≅ ∠BCQ [Common angle]
∴ ∆CPA ~ ∆CQB [AA test of similarity]
`therefore "AC"/"BC" = "AP"/"BQ"` [Corresponding sides of similar triangle]
`therefore "AC"/12 = 7/8`
`therefore "AC" = "x" = (12 xx 7)/8`
∴ AC = 10.5 units.
APPEARS IN
RELATED QUESTIONS
In figure, find ∠L
P and Q are points on sides AB and AC respectively of ∆ABC. If AP = 3 cm, PB = 6cm. AQ = 5 cm and QC = 10 cm, show that BC = 3PQ.
Given: ∠GHE = ∠DFE = 90°,
DH = 8, DF = 12,
DG = 3x – 1 and DE = 4x + 2.
Find: the lengths of segments DG and DE.
State the SSS-similarity criterion for similarity of triangles
In the given figure, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and AC is 14 cm. If arcs of equal radii 7 cm taking A, B, C and D as centres, have been drawn, then find the area of the shaded region ?
In the given figure, seg XY || seg BC, then which of the following statements is true?
In Δ ABC , MN || BC .
If BC = 14 cm and MN = 6 cm , find `("Ar" triangle "AMN")/("Ar" . ("trapezium MBCN"))`
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")`
A triangle ABC is enlarged, about the point O as centre of enlargement, and the scale factor is 3. Find : OA, if OA' = 6 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
PQ is perpendicular to BA and BD is perpendicular to AP.PQ and BD intersect at R. Prove that ΔABD ∼ ΔAPQ and `"AB"/"AP" = "BD"/"PQ"`.
In a quadrilateral PQRS, the diagonals PR and QS intersect each other at the point T. If PT:TR = QT :TS = 1:2, show that ΔPTQ - DRTS
In the given figure, PB is the bisector of ABC and ABC =ACB. Prove that:
a. BC x AP = PC x AB
b. AB:AC = BP: BC
Given is a triangle with sides 3 cm, 5 cm and 6 cm. Find the sides of a triangle which is similar to the given triangle and its shortest side is 4.5 cm.
The areas of two similar triangles are 169cm2 and 121cm2 respectively. If one side of the larger triangle is 26cm, find the length of the corresponding side of the smaller triangle.
ΔABC is enlarged, with a scale factor 5. Find: BC, f B'C' = 16cm
A model of a ship is made to a scale of 1:500. Find: The area other deck o the ship, if the area of the deck of its model is m2
Construct a triangle similar to a given triangle PQR with its sides equal to `7/3` of the corresponding sides of the triangle PQR (scale factor `7/3 > 1`)
ΔABC ~ ΔDEF. Write the ratios of their corresponding sides
Side of equilateral triangle PQR is 8 cm then find the area of triangle whose side is half of the side of triangle PQR.
