हिंदी

In Each of the Given Pairs of Triangles, Find Which Pair of Triangles Are Similar. State the Similarity Criterion and Write the Similarity Relation in Symbolic Form: - Mathematics

Advertisements
Advertisements

प्रश्न

In each of the given pairs of triangles, find which pair of triangles are similar. State the similarity criterion and write the similarity relation in symbolic form: 

उत्तर

We have: 

`CA/QR=8/6=4/3` and `6/4.5=4/3` 

⟹ `(CA)/(QR)=(CB)/(PQ)`
Also, ∠ACB = ∠PQR = 80°
Therefore, by SAS similarity theorem, Δ ACB - Δ RQP. 

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 4: Triangles - Exercises 2

APPEARS IN

आरएस अग्रवाल Mathematics [English] Class 10
अध्याय 4 Triangles
Exercises 2 | Q 1.3

संबंधित प्रश्न

Through the mid-point M of the side CD of a parallelogram ABCD, the line BM is drawn intersecting AC in L and AD produced in E. Prove that EL = 2 BL


Prove that the line segments joining the mid points of the sides of a triangle form four triangles, each of which is similar to the original triangle


Using Basic proportionality theorem, prove that a line drawn through the mid-points of one side of a triangle parallel to another side bisects the third side. (Recall that you have proved it in Class IX).


State, true or false:

Two congruent polygons are necessarily similar.


State, true or false:

All equiangular triangles are similar.


In the given triangle P, Q and R are the mid-points of sides AB, BC and AC respectively. Prove that triangle PQR is similar to triangle ABC.


In the given figure, ∠CAB = 90° and AD⊥BC. Show that ΔBDA ~ ΔBAC. If AC = 75cm, AB = 1m and BC = 1.25m, find AD. 

 


The corresponding altitudes of two similar triangles are 6cm and 9cm respectively. Find the ratio of their areas. 

 


State the SAS-similarity criterion 


In Figure 3, ABCD is a trapezium with AB || DC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. If arcs of equal radii 7 cm have been drawn, with centres A,B, C  and D, then find the area of the shaded region.


A ship is 400m laig and 100m wide. The length of its model is 20 cm. find the surface area of the deck of the model. 


The dimensions of the model of a multistorey building are 1.2 m × 75 cm × 2 m. If the scale factor is 1 : 30; find the actual dimensions of the building.


In the given figure, PQ || AB; CQ = 4.8 cm QB = 3.6 cm and AB = 6.3 cm. Find : If AP = x, then the value of AC in terms of x.


A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP.


In the given figure, ΔABC ~ ΔADE. If AE : EC = 4 : 7 and DE = 6.6 cm, find BC. If 'x' be the length of the perpendicular from A to DE, find the length of perpendicular from A to BC in terms of 'x'. 


Choose the correct alternative: 
If ΔABC ~ ΔPQR and 4A (ΔABC) = 25 A(ΔPQR), then AB : PQ = ? 


In ΔABC, point D divides AB in the ratio 5:7, Find: `"AE"/"AC"`


The diagonal AC of a parallelogram ABCD intersects DP at the point Q, where P is any point on side AB. Prove that CQ x PQ = QA x QD.


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


The areas of two similar triangles are 16cm2 and 9cm2 respectively. If the altitude of the smaller triangle is 1.8cm, find the length of the altitude corresponding to the larger triangle.


ΔABC has been reduced by a scale factor 0.6 to ΔA'B'C'/ Calculate:Length of B' C', if BC = 8cm


The scale of a map is 1 : 50000. The area of a city is 40 sq km which is to be represented on the map. Find: The length of a scale in km represented by 1cm on the map.


A map is drawn to scale of 1:20000. Find: The distance covered by 6cm on the map


A model of a ship is made to a scale of 1:500. Find: The volume of the model when the volume of the ship is 1km


In a triangle ABC, AB = 4 cm, BC = 4.5 cm and CA = 5 cm. Construct ΔABC. Find the image A'B'C of the ΔABC obtained by enlarging it by a scale factor 2. Measure the sides of the image A'B'C' and show that AB:A'B' = AC:B'C' = CA:C'A'


Construct a triangle similar to a given triangle ABC with its sides equal to `6/5` of the corresponding sides of the triangle ABC (scale factor `6/5 > 1`)


PR = 26 cm, QR = 24 cm, ∠PAQ = 90°, PA = 6 cm and QA = 8 cm. Find ∠PQR


If BD ⊥ AC and CE ⊥ AB, prove that `"CA"/"AB" = "CE"/"DB"`


Write the test of similarity for triangles given in figure.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×