हिंदी

From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.

Advertisements
Advertisements

प्रश्न

From the information shown in the figure, state the test assuring the congruence of ΔABC and ΔPQR. Write the remaining congruent parts of the triangles.

योग
Advertisements

उत्तर

In △ABC and △QPR

AB = PQ        ...(Given)

BC = PR          ...(Given)

∠BAC = ∠PQR = 90∘   ...(Given)

∴  ΔBAC ≅ ΔPQR       ...[Hypotenuse side test]

∴ seg AC ≅ seg QR      ...[c.s.c.t.]

∠ABC ≅ ∠QPR and ∠ACB ≅ ∠QRP    ...[c.a.c.t.]

shaalaa.com
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 3: Triangles - Practice Set 3.2 [पृष्ठ ३२]

APPEARS IN

बालभारती Mathematics 2 [English] Standard 9 Maharashtra State Board
अध्याय 3 Triangles
Practice Set 3.2 | Q 3. | पृष्ठ ३२

संबंधित प्रश्न

If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to ∠E 


If ΔDEF ≅ ΔBCA, write the part(s) of ΔBCA that correspond to `bar(EF)`


In a ΔABC, if AB = AC and ∠B = 70°, find ∠A. 


Prove that the sum of three altitudes of a triangle is less than the sum of its sides.


If ΔPQR≅ ΔEFD, then ∠E =


In an isosceles triangle, if the vertex angle is twice the sum of the base angles, then the measure of vertex angle of the triangle is


In the following example, a pair of triangles is shown. Equal parts of triangle in each pair are marked with the same sign. Observe the figure and state the test by which the triangles in each pair are congruent.

 By ______ test

ΔPRQ ≅ ΔSTU


In the given figure, ∠P ≅ ∠R seg, PQ ≅ seg RQ. Prove that, ΔPQT ≅ ΔRQS.


In the pair of triangles in the following figure, parts bearing identical marks are congruent. State the test and the correspondence of vertices by the triangle in pairs is congruent.


In the pair of triangles given below, the parts shown by identical marks are congruent. State the test and the one-to-one correspondence of vertices by which the triangles in the pair are congruent, the remaining congruent parts.


The following figure shown a triangle ABC in which AB = AC. M is a point on AB and N is a point on AC such that BM = CN.

Prove that:  


In a triangle, ABC, AB = BC, AD is perpendicular to side BC and CE is perpendicular to side AB. Prove that: AD = CE.


State, whether the pairs of triangles given in the following figures are congruent or not:

   


Prove that:
(i) ∆ ABC ≅ ∆ ADC
(ii) ∠B = ∠D


State, whether the pairs of triangles given in the following figures are congruent or not:


Which of the following pairs of triangles are congruent? Give reasons
ΔABC;(AB = 8cm,BC = 6cm,∠B = 100°);
ΔPQR;(PQ = 8cm,RP = 5cm,∠Q = 100°).


In the figure, AC = AE, AB = AD and ∠BAD = ∠EAC. Prove that BC = DE.


If ∆PQR is congruent to ∆STU (see figure), then what is the length of TU?


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×