Congruence of Triangles - Solutions 1

CBSE Class –VII Mathematics
NCERT Solutions
Chapter 7 Congruence of Triangles (Ex. 7.1)

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Question 1. Complete the following statements:

1. Two line segments are congruent if _______________.
2. Among two congruent angles, one has a measure of 70∘,${70}^{\circ },$ the measure of other angle is _______________.
3. When we write ∠$\mathrm{\angle }$A = ∠$\mathrm{\angle }$B, we actually mean _______________.

Answer: (a) they have the same length

(b) 70∘${70}^{\circ }$

(c) m∠$m\mathrm{\angle }$A = m∠$m\mathrm{\angle }$B

Question 2. Give any two real time examples for congruent shapes.

Answer: (i) Two footballs

(ii) Two teacher’s tables

Question 3. If Δ$\mathrm{\Delta }$ABC ≅Δ$\cong \mathrm{\Delta }$FED under the correspondence ABC ↔$\leftrightarrow$ FED, write all the corresponding congruent parts of the triangles.

Answer: Given: Δ$\mathrm{\Delta }$ABC ≅$\cong$Δ$\mathrm{\Delta }$FED.

The corresponding congruent parts of the triangles are:

(i) ∠$\mathrm{\angle }$A ↔$\leftrightarrow$∠$\mathrm{\angle }$F

(ii) ∠$\mathrm{\angle }$B ↔$\leftrightarrow$∠$\mathrm{\angle }$E

(iii) ∠$\mathrm{\angle }$C ↔$\leftrightarrow$∠$\mathrm{\angle }$D

(iv) AB¯¯¯¯¯¯¯$\overline{\text{AB}}$↔$\leftrightarrow$FE¯¯¯¯¯¯¯$\overline{\text{FE}}$

(v) BC¯¯¯¯¯¯¯$\overline{\text{BC}}$↔$\leftrightarrow$ED¯¯¯¯¯¯¯$\overline{\text{ED}}$

(vi) AC¯¯¯¯¯¯¯$\overline{\text{AC}}$↔$\leftrightarrow$FD¯¯¯¯¯¯¯$\overline{\text{FD}}$

Question 4. If Δ$\mathrm{\Delta }$DEF ≅Δ$\cong \mathrm{\Delta }$BCA, write the part(s) of Δ$\mathrm{\Delta }$BCA that correspond to:

i.∠$\mathrm{\angle }$E

ii.EF¯¯¯¯¯¯¯$\overline{\text{EF}}$

iii.∠$\mathrm{\angle }$F

iv.DF¯¯¯¯¯¯¯$\overline{\text{DF}}$

Answer: Given: Δ$\mathrm{\Delta }$DEF ≅$\cong$Δ$\mathrm{\Delta }$BCA.

(i) ∠$\mathrm{\angle }$E ↔$\leftrightarrow$∠$\mathrm{\angle }$C

(ii) EF¯¯¯¯¯¯¯$\overline{\text{EF}}$↔$\leftrightarrow$CA¯¯¯¯¯¯¯$\overline{\text{CA}}$

(iii) ∠$\mathrm{\angle }$F ↔$\leftrightarrow$∠$\mathrm{\angle }$A

(iv) DF¯¯¯¯¯¯¯$\overline{\text{DF}}$↔$\leftrightarrow$BA¯¯¯¯¯¯¯