<ol class="num-list"><li><div class="list-item-paragraph">Congruent triangles have exactly the same shape and size.</div></li><li><div class="list-item-paragraph">Properties of congruent triangles are:</div><div class="list-item-paragraph">•	equal corresponding angles</div><div class="list-item-paragraph">•	equal corresponding sides</div></li><li><div class="list-item-paragraph">The symbol for congruency is ‘\(\equiv \)’.</div></li><li><div class="list-item-paragraph">Congruency Tests for Triangles</div><div class="table-container"><table><colgroup><col style="width: 300px;"><col style="width: 300px;"></colgroup><thead><tr style="height: 30px;"><th style="height: 30px; min-height: 30px; text-align: left; --cell-justify: flex-start"><p><strong><u>SSS Congruency Test</u></strong></p><p style="text-align: center;"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767488761082-0q8631rgyd8m.png" data-width="75%" style="width: 75%; max-width: 75%;"></p></th><th style="height: 30px; min-height: 30px; text-align: center; --cell-justify: center"><p style="text-align: center;">\(AB=XY\),</p><p style="text-align: center;">\(BC=YZ\),</p><p style="text-align: center;">\(AC=XZ\).</p><p style="text-align: center;">\[\therefore \Delta ABC \equiv \Delta XZY\]</p><p style="text-align: center;">(\(\text{SSS}\) Congruency Test)</p></th></tr></thead><tbody><tr style="height: 30px;"><td style="height: 30px; min-height: 30px; text-align: left; --cell-justify: flex-start"><p><strong><u>SAS Congruency Test</u></strong></p><p style="text-align: center;"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767488813638-r34luc7xfcq.png" data-width="75%" style="width: 75%; max-width: 75%;"></p></td><td style="height: 30px; min-height: 30px; text-align: center; --cell-justify: center"><p>\(AB=XZ\),</p><p>\(BC=ZY\),</p><p>\(\angle ABC=\angle XZY\) (Included Angle)</p><p>\[\therefore \Delta ABC \equiv \Delta YZX\]</p><p>(\(\text{SAS}\) Congruency Test)</p></td></tr><tr style="height: 30px;"><td style="height: 30px; min-height: 30px; text-align: left; --cell-justify: flex-start"><p><strong><u>AAS Congruency Test</u></strong></p><p style="text-align: center;"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767488844496-ajy1inxqnif.png" data-width="75%" style="width: 75%; max-width: 75%;"></p></td><td style="height: 30px; min-height: 30px; text-align: center; --cell-justify: center"><p>\(PQ=YX\),</p><p>\(\angle PQR=\angle YXZ\),</p><p>\(\angle PRQ=\angle YZX\),</p><p>\[\therefore \Delta PQR \equiv \Delta YXZ\]</p><p>(\(\text{AAS}\) Congruency Test)</p></td></tr><tr style="height: 30px;"><td style="height: 30px; min-height: 30px; text-align: left; --cell-justify: flex-start"><p><strong><u>RHS Congruency Test</u></strong></p><p style="text-align: center;"><img class="rich-text-image" src="https://vocwkpgapvksartxhhor.supabase.co/storage/v1/object/public/question-images/pasted/1767488867269-r01qi1w16zk.png" data-width="75%" style="width: 75%; max-width: 75%;"></p></td><td style="height: 30px; min-height: 30px; text-align: center; --cell-justify: center"><p>\(AC=DE\),</p><p>\(AB=DF\),</p><p>\(\angle ABC=\angle DFE\)</p><p>\[\therefore \Delta ABC \equiv \Delta DFE\]</p><p>(\(\text{RHS}\) Congruency Test)</p></td></tr></tbody></table></div></li><li><div class="list-item-paragraph">The most important things that you have to take notes when proving a pair of congruent triangles:</div><div class="list-item-paragraph">•	To list down the \(3\) equivalent corresponding angles or corresponding sides and give reasons or justifications necessary.</div><div class="list-item-paragraph">•	Never make assumptions if questions did not state so.</div><div class="list-item-paragraph">•	To write down the test property (\(\text{SSS}\), \(\text{SAS}\), \(\text{AAS}\) or \(\text{RHS}\)).</div><div class="list-item-paragraph">•	<strong>Order</strong> of naming a pair of congruent triangles is important.</div></li></ol>

Congruent triangles have exactly the same shape and size.

The symbol for congruency is ‘\(\equiv \)’.

The most important things that you have to take notes when proving a pair of congruent triangles:

•	To list down the \(3\) equivalent corresponding angles or corresponding sides and give reasons or justifications necessary.

•	Never make assumptions if questions did not state so.

•	To write down the test property (\(\text{SSS}\), \(\text{SAS}\), \(\text{AAS}\) or \(\text{RHS}\)).

Congruency and Similarity - Congruence

Question 27265d58

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