and sides between congruent triangles basing on the fact that - PowerPoint PPT Presentation

D AY 62 – C ONGRUENT ANGLES AND SIDES

I NTRODUCTION The most important parts of the triangle that we consider here are sides and three angles. Congruent triangles have corresponding sides of the same length and corresponding angles with equal measures. This means that congruent triangles have matching parts. We have also dealt with triangle congruence postulates; S.S.S, S.A.S, and A.S.A to determine triangle congruence. In this lesson, we are going to summarize the concept of identifying congruent angles and sides from congruent triangles.

V OCABULARY 1. Congruent Angles Angles that have the same measure 2. Congruent Sides Sides that have the same length 3. Corresponding parts of congruent triangles Parts in the same position in relation to the parts in the other congruent triangle.

Our main aim is to identify congruent angles and sides between congruent triangles basing on the fact that corresponding parts in congruent triangles are congruent. When identifying congruent angles and sides in congruent triangles, we match angles and sides of one triangle to the angles and sides of the other triangle, that is, we identify pairs of corresponding parts. We usually use the statement “corresponding parts of congruent triangles are congruent” which is abbreviated as CPCTC

In order to identify the corresponding angles and sides, we first identify corresponding parts, that is, we identify corresponding angles and sides. Correspondence is important because it helps us know which sides are congruent and which angles have the same measure because in most cases the triangles are congruent, but the orientation varies.

C ONGRUENT TRIANGLES ΔABC and ΔKLM shown below are congruent, therefore, their corresponding parts will be congruent. K A C M L B

In order to identify congruent angles and sides: 1. We first identify corresponding vertices Considering ΔABC and ΔKLM above, the following are pairs of corresponding vertices paying attention to correct correspondence due to different orientations. B and K C and L A and M

2. Then we identify corresponding angles The following are pairs of corresponding angles based on correct correspondence. ∠B and ∠K ∠C and ∠L ∠A and ∠M 3. We identify corresponding sides The following are pairs of corresponding sides based on correspondence. AC and ML ; BC and KL ; AB and MK

4. The corresponding angles and sides are congruent, therefore, congruent angles are: ∠B and ∠K ∠C and ∠L ∠A and ∠M Similarly, congruent sides are: AC and ML BC and KL AB and MK

Example Given that ΔPQR below and ΔSTU are congruent. Find the length of QR and hence find the perimeter of ΔSTU . P U 3.5 in. 2.5 in. 79° S 22° R 79° Q U

Solution Since the triangles are congruent, they have congruent parts. ΔSTU has two angles of 79° each, it must be isosceles. This means that ΔPQR is also isosceles. Recall that the angle sum of a triangle is 180° . 79° + 79° + 22° = 180° We have, QP = 𝐑𝐒 = 𝟒. 𝟔 𝐣𝐨. Now, the perimeter of ΔSTU = 3.5 + 2.5 + 3.5 = 𝟘. 𝟔 𝐣𝐨.

HOMEWORK Given that ΔKLM ≅ ΔXYZ , use the correct correspondence to identify an angle in ΔXYZ that is congruent to ∠K in ΔKLM and a side in ΔKLM that is congruent to YX in ΔXYZ . X K M Z Y L

A NSWERS TO HOMEWORK ∠K and KM

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