English
Maharashtra State BoardSSC (English Medium) 9th Standard

As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

Advertisements
Advertisements

Question

As shown in the following figure, in ΔLMN and ΔPNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.

Sum
Advertisements

Solution

​In △LMN and △PNM

seg LM ≅ seg PN

seg LN ≅ seg PM         ...(Given)

seg MN ≅ seg NM       ...(Common side)

△LMN ≅ △PNM          ...(SSS test)

`{:("∠LMN ≅ ∠PNM"), ("∠MLN ≅ ∠NPM"), ("∠LNM ≅ ∠PMN"):} }  ...("c.a.c.t.")`

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Triangles - Practice Set 3.2 [Page 32]

APPEARS IN

Balbharati Mathematics 2 [English] Standard 9 Maharashtra State Board
Chapter 3 Triangles
Practice Set 3.2 | Q 4. | Page 32

RELATED QUESTIONS

If ΔABC ≅ ΔFED under the correspondence ABC ↔ FED, write all the Corresponding congruent parts of the triangles.


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


Mark the correct alternative in each of the following:

If ABC ≅  ΔLKM, then side of ΔLKM equal to side AC of ΔABC is


If ABC and DEF are two triangles such that ΔABC \[\cong\] ΔFDE and AB = 5cm, ∠B = 40°


In the given figure, ABC is a triangle in which ∠B = 2∠C. D is a point on side BC such that ADbisects ∠BAC and AB = CD. BE is the bisector of ∠B. The measure of ∠BAC is


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.


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.


In the following diagram, ABCD is a square and APB is an equilateral triangle.

(i) Prove that: ΔAPD≅ ΔBPC
(ii) Find the angles of ΔDPC.


In the following diagram, AP and BQ are equal and parallel to each other. 

Prove that:  

  1. ΔAOP ≅ ΔBOQ.
  2. AB and PQ bisect each other.

The following figure has 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: (i) BN = CM (ii) ΔBMC ≅ ΔCNB   


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:  


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


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


In the given figure, prove that: ∆ ABD ≅ ∆ ACD


In a triangle ABC, if D is midpoint of BC; AD is produced upto E such as DE = AD, then prove that:
a. DABD andDECD are congruent.
b. AB = EC
c. AB is parallel to EC


In the given figure ABCD is a parallelogram, AB is Produced to L and E is a midpoint of BC. Show that:

a. DDCE ≅ DLDE
b. AB = BL
c. DC = `"AL"/(2)`


In ΔABC, AB = AC, BM and Cn are perpendiculars on AC and AB respectively. Prove that BM = CN.


ΔABC is an isosceles triangle with AB = AC. GB and HC ARE perpendiculars drawn on BC.

Prove that 
(i) BG = CH
(ii) AG = AH


If the given two triangles are congruent, then identify all the corresponding sides and also write the congruent angles


Without drawing the triangles write all six pairs of equal measures in the following pairs of congruent triangles.

∆STU ≅  ∆DEF


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×