Question

Ex. (4)
P Р
In the adjoining figure BPL AC, CO LAB,
A-P-CA-Q-B, then prove that
A APB and A AQC are similar.
Solution
In A APB and AAC
Z APB =
LAQC = T (1)
2 APB ZAQC ....from() and (ID)
Z PAB = L QAC...
B
C С
​

Answer 1

2. SAS test for similarity of triangles: For a given correspondence, if two pairs of corresponding sides are in the same proportion and the angle between them is congruent, then the two triangles are similar. In the given figure, if AB/PQ = BC/QR, and ∠B ≅∠Q, then ∆ABC ~ ∆PQR 3. SSS test for similarity of triangles: For a given correspondence, if three sides of one triangle are in proportion with the corresponding three sides of the another triangle, then the two triangles are similar. In the given figure, of AB/PQ = BC = QR = AC/PR, then ∆ABC ~ ∆PQR Properties of similar triangles: 1. Reflexivity: ∆ABC ~ ∆ABC 2. Symmetry : If ∆ABC ~ ∆DEF, then ∆DEF ~ ∆ABC. 3. Transitivity: If ∆ABC ~ ∆DEF and ∆DEF ~ ∆GHI, then ∆ABC ~ ∆GHI.