Notes
Practice Set 13.1
Question 1.1. 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) The triangles are congruent by SAS test under the correspondence XWZ ↔ YWZ.
(ii) The triangles are congruent by hypotenuse side test under the correspondence KJI ↔ LJI.
(iii) The triangles are congruent by SSS test under the correspondence HEG ↔ FGE.
(iv) The triangles are congruent by ASA test under the correspondence SMA↔ OPT.
(v) The triangles are congruent by SAA test under the correspondence MTN ↔ STN.
Practice Set 13.2
Question 2.1. In each pair of triangles given below, parts shown by identical marks are congruent. State the test and the one to one correspondence of vertices by which triangles in each pair are congruent and remaining congruent parts.
In Δ MST and Δ TBM,
side MS ≅ side TB ….(given)
∠ MST ≅ ∠ TBM …..(right angle)
side MT is common
∴ By Hypotenuse-side test, Δ MST ≅ Δ TBM.
∴ side ST ≅ side MB,
∠ SMT ≅ ∠ BTM,
∠ STM ≅ ∠ BMT
In Δ PRQ and Δ TRS,
side PR ≅ side RT …..(given)
side QR ≅ side RS …..(given)
∠ PRQ ≅ ∠SRT ……(vertically opposite angles)
∴ By the SAS test, Δ PRQ ≅ Δ TRS.
∴ side PQ ≅ side ST,
∠ QPR ≅ ∠ STR,
∠ PQR ≅ ∠ TSR.
In Δ DHC and Δ DFC,
∠ DCH ≅ ∠ DCF ….(given)
∠ DHC ≅ ∠ DFC ….(given)
side DC is common
∴ By AAS test, Δ DHC ≅ Δ DFC.
∴ side DH ≅ side DF,
side HC ≅ side FC,
∠ HDC ≅ ∠ FDC.
Question 2.2. In the adjacent figure, seg AD ≅ seg EC Which additional information is needed to show that Δ ABD and Δ EBC will be congruent by A-A-S test ?
In Δ ABD and Δ EBC,
side AD ≅ side EC ... [Given]
∠ ABD ≅ ∠EBC ... [vertically opposite angles]
: To show that Δ ABD and Δ EBC will be congruent by A-A-S test, one of the following is needed:
∠ BAD ≅ ∠ BCE or ∠ BDA ≅ ∠ BEC