Practice Set 3.2 Geometry 9th Std Maths Part 2 Answers Chapter 3 Triangles
Question 1
Maharashtra Board Solution
In each of the examples given below, a pair of triangles is shown. Equal parts of triangles in each pair are marked with the same signs. Observe the figures and state the test by which the triangles in each pair are congruent. By SSS test ∆ABC ≅ ∆PQR
By SAS test
∆ XYZ ≅ ∆LMN
By ASA test
∆PRQ ≅ ∆STU
By hypotenuse side test
∆LMN ≅ ∆PTR
Question 2
Maharashtra Board Solution
Observe the information shown in pairs of triangles given below. State the test by which the two triangles are congruent. Write the remaining congruent parts of the triangles.
Solution & Step-by-Step Answer:
block bg-white dark:bg-slate-900/80 border-l-4 border-emerald-500 rounded-r-xl p-5 my-3 shadow-xs border border-slate-200/60 dark:border-slate-800">
Solution & Step-by-Step Answer:
From the information shown in the figure, In ∆ABC and ∆PQR, ∠ABC ≅ ∠PQR seg BC ≅ seg QR ∠ACB ≅ ∠PRQ ∴ ∆ABC ≅ ∆PQR [ASA test] ∴ ∠BAC ≅ ∠QPR [Corresponding angles of congruent triangles] seg AB ≅ segPQ and segAC ≅ seg PR [Corresponding sides of congruent triangles]
Question 3
Maharashtra Board Solution
From the information shown in the figure, state the test assuring the congruence of ∆ABC and ∆PQR. Write the remaining congruent parts of the triangles.
Solution & Step-by-Step Answer:
In ∆BAC and ∆PQR, seg BA ≅ seg PQ seg BC ≅ seg PR ∠BAC ≅ ∠PQR = 90° [Given] ∴ ∆BAC ≅ ∆PQR [Hypotenuse side test] ∴ seg AC ≅ seg QR [c.s.c.t.] ∠ABC ≅ ∠QPR and ∠ACB ≅ ∠QRP [c.a.c.t.]
Question 4
Maharashtra Board Solution
As shown in the adjoining figure, in ∆LMN and ∆PNM, LM = PN, LN = PM. Write the test which assures the congruence of the two triangles. Write their remaining congruent parts.
Solution & Step-by-Step Answer:
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, and ∠LNM ≅ ∠PMN [c.a.c.t.]
Question 5
Maharashtra Board Solution
In the adjoining figure, seg AB ≅ seg CB and seg AD ≅ seg CD. Prove that ∆ABD ≅ ∆CBD.
Solution & Step-by-Step Answer:
proof: In ∆ABD and ∆CBD, seg AB ≅ seg CB seg AD ≅ seg CD [Given] seg BD ≅ seg BD [Common side] ∴ ∆ABD ≅ ∆CBD [SSS test]
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