Question

In the adjoining figure BP|AC,CQ|AB, A-P-C ,A-Q-B ,then prove that angleAPB and angle AQC are similar​

Answer 1

Answer:

See the attached picture

Step-by-step explanation:

❤️ Hope this helps you ❤️

Answer 2

Answer:

1. proff

In ∆ APB and ∆ AQC

angleAPB = 90° (1)

angle AQC = 90° (2)

angleAPB ≈ angle AQC [ from (1) and (2) ]

angleAPB ≈ angle QAC [ common angle ]

∆APB ~ ∆AQC [ AA test of similarity ]

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.

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