Question

Please don’t answer if you don’t understand this

Name the angles and sides of each pair of triangles that are congruent.

Answer 1

Corresponding parts are congruent

ΔGHF ≅ ΔGHL

Congruent parts:

Sides

• GH ≅ GH, HF ≅ HL, GF ≅ GL

Angles in simple form

• ∠H ≅ ∠H, ∠F ≅ ∠L, ∠G ≅ ∠G

Angles in full format

• ∠GHF ≅ ∠GHL, ∠GFH ≅ ∠GLH, ∠FGH ≅ ∠LGH

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ΔWXY ≅ ΔDCY

Congruent parts:

Sides

• WX ≅ DC, XY ≅ CY, WY ≅ DY

Angles in simple form

• ∠X ≅ ∠C, ∠Y ≅ ∠Y, ∠W ≅ ∠D

Angles in full format

• ∠WXY ≅ ∠DCY, ∠WYX ≅ ∠DYC, ∠XWY ≅ ∠CDY

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ΔCBD ≅ ΔJKL

Congruent parts:

Sides

• CB ≅ JK, BD ≅ KL, CD ≅ JL

Angles in simple form

• ∠B ≅ ∠K, ∠D ≅ ∠L, ∠C ≅ ∠J

Angles in full format

• ∠CBD ≅ ∠JKL, ∠CDB ≅ ∠JLK, ∠BCD ≅ ∠KJL

Answer 2

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Answer:

1. angles: ∠GHF≅∠GHL, ∠F≅∠L, ∠FGH≅∠LGH; sides: GH≅GH, GF≅GL, HF≅HL
2. angles: ∠W≅∠D, ∠X≅∠C, ∠XYW≅∠CYD; sides: WX≅DC, WY≅DY, XY≅CY
3. angles:∠C≅∠J, ∠B≅∠K, ∠D≅∠L; sides: CB≅JK, CD≅JL, BD≅KL

Explanation:

The key with naming corresponding parts is to use the congruence (or similarity) statement. Corresponding vertices are those that are in the same position in the congruence statement, regardless of what the figure may look like.*

Angles can be named using the letter at its vertex--if there is only one angle with that vertex--or using three letters. The three letters name a point on one ray, the vertex, and a point on the other ray. When naming corresponding angles from a congruence statement, it is nice (but not absolutely essential) to name the corresponding rays in the same order. In any event, the named vertices must be corresponding.

Sides are named using two letters--the points at the end of the side. The points used to name corresponding sides must come from the same positions in the congruence statement. Technically, side named AB is the same as side BA, but it is nice to use corresponding points in the same order when naming corresponding sides. Example: in the first figure, CB≅JK, but it is also true that BC≅JK because CB can be named either as CB or BC. In both cases, the points named are the 1st and 2nd in the congruence statements.

In the answer section above, we have used 3-letter angles where a vertex is shared by two or more angles. We have used single-letter names for angles where there is no ambiguity. When asked to name all the names, as here, it is best to make use of a pattern you understand. For angles, we worked left-to-right down the congruence statement; for sides we used the pattern 12, 13, 23 for the positions of the letters in the congruence statement.

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* Sometimes, poorly-edited curriculum materials will misstate the congruence statement. It is best to report the problem to your teacher in those cases. Sometimes, the figure is intentionally misleading (as in the second problem here). For those, you must pay careful attention to the congruence statement.