State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).
∆ PQR : PQ = 3.5 cm, QR = 4.0 cm, ∠ Q = 60° ∆ STU : ST = 3.5 cm, TU = 4 cm, ∠ T = 60°
Solution:
Given, PQR and STU Z are a pair of triangles.
We have to determine if the given pairs of triangles are congruent and write them in symbolic form.
In triangle PQR,
PQ = 3.5 cm and QR = 4.0 cm
∠Q = 60°
In triangle STU,
ST = 3.5 cm and TU = 4 cm
∠T = 60°
We observe that two sides and the angle included between them are equal.
The SAS criterion states that If two sides of one triangle are respectively proportional to two corresponding sides of another, and if the included angles are equal, then the two triangles are congruent.
By SAS rule, ∆PQR ≅ ∆STU
✦ Try This: State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure).
∆XYZ : XY = 4.2 cm, YZ = 2.0 cm, ∠Y = 70° ∆DEF : DE = 4.2 cm, EF = 2 cm, ∠E = 60°
☛ Also Check: NCERT Solutions for Class 7 Maths Chapter 6
NCERT Exemplar Class 7 Maths Chapter 6 Problem 149 (a)
State which of the following pairs of triangles are congruent. If yes, write them in symbolic form (you may draw a rough figure). ∆ PQR : PQ = 3.5 cm, QR = 4.0 cm, ∠ Q = 60° ∆ STU : ST = 3.5 cm, TU = 4 cm, ∠ T = 60°
Summary:
The given triangles are congruent. The symbolic form is ∆PQR ≅ ∆STU.
☛ Related Questions:
- State which of the following pairs of triangles are congruent. If yes, write them in symbolic form ( . . . .
- In Fig. 6.51, PQ = PS and ∠1 = ∠2. (i) Is ∆PQR ≅ ∆PSR? Give reasons. (ii) Is QR = SR? Give reasons
- In Fig. 6.52, DE = IH, EG = FI and ∠ E = ∠ I. Is ∆DEF ≅ ∆HIG? If yes, by which congruence criterion