Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1

Maharashtra State Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1

Congruence of Triangles Practice Set 13.1 Question 1.
In each pair of triangles in the following figures, parts bearing identical marks are congruent. State the test and correspondence of vertices by which triangles in each pair are congruent.
i.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 1
ii.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 2
iii.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 3
iv.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 4
v.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 5
Solution:
i.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 6
The two triangles are congruent by SAS test in the correspondence XWZ ↔ YWZ.

ii.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 7
The two triangles are congruent by hypotenuse-side test in the correspondence KJI ↔ LJI.

iii.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 8
The two triangles are congruent by SSS test in the correspondence HEG ↔ FGE.

iv.
The two triangles are congruent by ASA test is the correspondence SMA ↔ OPT.

v.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 9
The two triangles are congruent by ASA test or SAS test or SAA test in the correspondence MTN ↔ STN.

Maharashtra Board Class 8 Maths Chapter 13 Congruence of Triangles Practice Set 13.1 Intext Questions and Activities

Practice Set 13.1 Question 1.
Write answers to the following questions referring to the given figure.
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 10

  1. Which is the angle opposite to the side DE?
  2. Which is the side opposite to ∠E?
  3. Which angle is included by side DE and side DF?
  4. Which side is included by ∠E and ∠F?
  5. State the angles adjacent to side DE. (Textbook pg, no. 81)

Solution:

  1. ∠DFE i.e. ∠F is the angle opposite to side DE.
  2. Side DF is the side opposite to ∠E.
  3. ∠EDF i.e. ∠D is included by side DE and side DF.
  4. Side EF is included by ∠E and ∠F.
  5. ∠DEF and ∠EDF i.e. ∠E and ∠D are adjacent to side DE.

Congruence of Triangles Class 8th Practice Set 13.1 Question 2.
In the given figure, parts of triangles indicated by identical marks are congruent.
a. Identify the one-to-one correspondence of vertices in which the two triangles are congruent and write the congruence.
b. State with reason, whether the statement, ∆XYZ ≅ ∆STU is right or wrong. (Textbook pg. no. 82)
Maharashtra Board Class 8 Maths Solutions Chapter 13 Congruence of Triangles Practice Set 13.1 11
Solution:
a. From the figure,
S ↔ X, T ↔ Z, U ↔ Y i.e.,
STU ↔ XZY, or SUT ↔ XYZ, or
TUS ↔ ZYX, or TSU ↔ ZXY, or
UTS ↔ YZX, or UST ↔ YXZ

∴ ∆STU ≅ ∆XZY, or ∆SUT ≅ ∆XYZ, or
∆TUS ≅ ∆ZYX, or ∆TSU ≅ ∆ZXY, or
∆UTS ≅ ∆YZX, or ∆UST ≅ ∆YXZ

b. If ∆XYZ ≅ ∆STU, then
∠Y ≅ ∠T, ∠Z ≅ ∠U,
seg XY ≅ seg ST, seg XZ ≅ seg SU
∴ But, all the above statements are wrong. The statement AXYZ ≅ ASTU is wrong.

Maharashtra Board Class 8 Maths Solutions

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