Geomentry help | Similar Triangle Basics | Proving triangles are similar
Two triangles are similar, if (i) their corresponding angles are equal and (ii) their corresponding sides are in the same ratio (or proportion).
Similarity postulates AA SAS SSS
AAA similarity criterion
If two angles of one triangle are respectively equal to two angles of another triangle, then the two triangles are similar.
SSS (Side–Side–Side) similarity criterion for two triangles
If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similiar.
SAS (Side–Angle–Side) similarity criterion for two triangles
If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar
00:03 CBSE class 10 maths NCERT Solutions chapter 6 Triangles Q1. State which pairs of triangles in Fig. 6.34 are similar. Write the similarity criterion used by you for answering the question and also write the pairs of similar triangles in the symbolic form :
00:47 Tests for Similar Triangles AA similarity criterion
01:18 (ii) | 02:58 (iii) | 03:59 (iv) | 04:56 (v) | 06:10 (vi) |
02:18 Solving similar triangles SSS (Side–Side–Side) similarity criterion
05:44 SAS (Side–Angle–Side) similarity criterion for two triangles
06:35 Angle sum prpperty of triangle.
07:23 Solving similar triangles AA similarity criterion
07:46 CBSE class 10 maths NCERT Solutions chapter 6 Triangles Q3. Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point O. Using a similarity criterion for two triangles, show that OA/OC = OB/OD.
08:15 constructions procedure to solve geometry problems
09:21 Vertically opposite angles are equal
09:34 Alrenate interior angles
10:17 AAA similarity criterion
11:04 CBSE class 10 maths NCERT Solutions chapter 6 Triangles Q4. In Fig. 6.36, QR/QS = QT/PR and angle 1 = angle 2. Show that triangle PQS ~ triangle TQR.
12:02 It tow angles are equal then their sides opposite to equal angles are equal.
13:54 SAS (Side–Angle–Side) similarity criterion for two triangles
14:13 CBSE class 10 maths NCERT Solutions chapter 6 Triangles Q5. S and T are points on sides PR and QR of triangle PQR such that angle P = angle RTS. Show that triangle RPQ ~ triangle RTS.
16:07 AAA similarity criterion
16:37 Q6. In Fig. 6.37, if triangle ABE ~ triangle ACD, show that triangle ADE ~ triangle ABC.
18:35 SAS (Side–Angle–Side) similarity criterion
19:32 Q7. In Fig. 6.38, altitudes AD and CE of triangle ABC intersect each other at the point P. Show that:
20:35 (i) triangle AEP ~ triangle CDP
21:14 Vertically opposite angles are equal
22:09 (ii) triangle ABD ~ triangle CBE
22:54 use AAA similarity criterion
23:39 (iii) triangle AEP ~ triangle ADB
25:05 AAA similarity criterion
25:36 (iv) triangle PDC ~ triangle BEC
26:19 AA similarity criterion
26:37 CBSE class 10 maths NCERT Solutions chapter 6 Triangles Q8. E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that triangle ABE ~ triangle CFB.
28:51 Apply AA similarity criterion.
29:40 Q9. In Fig. 6.39, ABC and AMP are two right triangles, right angled at B and M respectively. Prove that:
30:07 (i) triangle ABC ~ triangle AMP 31:23 (ii) CA/PA = BC/MP.
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