Triangles similarity and congruence

The shape of a triangle is determined up to congruence by specifying two sides and the angle between them SAStwo angles and the side between them ASA or two angles and a corresponding adjacent side AAS. Specifying two sides and an adjacent angle SSAhowever, can yield two distinct possible triangles.

Triangles similarity and congruence

What is "Congruent" ... ?

As you can see in the unit Enlargement, Angle and Length, enlargement An enlargement is a type of transformation in which lengths are multiplied whilst directions and angles are preserved. The transformation is specified by a scale factor of enlargement and a centre of enlargement.


For every point in the original shape, the transformation multiplies the distance between the point and the centre of enlargement by the scale factor. So mathematically, any original shape and its enlarged image are similar.

The model in Fig. The scale factor of enlargement is shown between them. You can type in a new scale factor of enlargement to see the second shape change size, or use the handle on the image A shape that is the result of a transformation on the coordinate plane.

Click on the figure below to interact with the model. Two shapes related by enlargement. Although the size of a shape changes during enlargement, it remains in proportion to the original shape.

That is, although the new shape is a different size from the original, it retains the same proportions. This is a useful aspect of similarity. In fact, it means that we can use whether shapes are in proportion to one another as a test for similarity.

Triangles similarity and congruence

For instance, look at the two triangles in Fig. Marked on them are all the measurements that we know of them. To find out, we first identify what would would be the corresponding sides if the triangles were similar.How To Find if Triangles are Congruent: Two triangles are congruent if they have: If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent.

5. Congruent Congruent Triangles Similar Similar Triangles Finding Similar Triangles .

Proving Similarity of Triangles

Get ahead in the class with FREE content! Learnhive detects learning gaps & guides students to do better. Use our FREE online learning materials (Math, Science, & English) for Class 1 to Similarity & Congruence (H) - Version 2 January Similarity & Congruence (H) A collection of Maths GCSE Sample and Specimen questions from AQA, OCR, Pearson-Edexcel and WJEC Eduqas.

Triangles similarity and congruence

Index for Geometry Math terminology from plane and solid geometry. This includes basic triangle trigonometry as well as a few facts not traditionally taught in basic geometry. The congruence theorems side-angle-side (SAS) and side-side-side (SSS) also hold on a sphere; in addition, if two spherical triangles have an identical angle-angle-angle (AAA) sequence, they are congruent (unlike for plane triangles).

Two triangles are congruent if their corresponding sides are equal in length, and their corresponding angles are equal in measure.. If triangle ABC is congruent to triangle DEF, the relationship can be written mathematically as: ≅.

In many cases it is sufficient to establish the equality of three corresponding parts and use one of the following results to deduce the congruence of the two.

SparkNotes: Geometry: Congruence: Proving Similarity of Triangles