Geometry worksheet focusing on identifying corresponding sides and angles in congruent triangles.

To solve these problems, we use the rule that congruent triangles are identical in shape and size. This means:
1. Corresponding Angles are equal (e.g., $\angle A = \angle D$).
2. Corresponding Sides are equal in length (e.g., side $AB$ = side $DE$).

The order of the letters in the triangle names tells us which parts match up. For example, if $\triangle ABC \cong \triangle DEF$, then $A$ matches $D$, $B$ matches $E$, and $C$ matches $F$.

Here is the step-by-step solution for each problem:

Problem 1: $\triangle ABC \cong \triangle DEF$

Matching Parts:
* Angle $A$ corresponds to Angle $D$.
* Angle $B$ corresponds to Angle $E$.
* Angle $C$ corresponds to Angle $F$.
* Side $AB$ corresponds to Side $DE$.
* Side $BC$ corresponds to Side $EF$.
* Side $CA$ corresponds to Side $FD$.

Finding Values from the Diagram ($\triangle DEF$):
* Side $DE = 15$ cm
* Side $EF = 12$ m (Note: The diagram says "m", likely meters, but usually these are consistent units. We will just copy the number given).
* Side $FD = 7$ cm
* Angle $D = 40^\circ$
* Angle $E = 60^\circ$
* Angle $F = 80^\circ$

Filling in the blanks:
* $AB = DE = \mathbf{15}$ cm
* $DE = \mathbf{15}$ cm
* $\angle A = \angle D = \mathbf{40}^\circ$
* $\angle D = \mathbf{40}^\circ$
* $BC = EF = \mathbf{12}$ m
* $EF = \mathbf{12}$ m
* $\angle B = \angle E = \mathbf{60}^\circ$
* $\angle E = \mathbf{60}^\circ$
* $CA = FD = \mathbf{7}$ cm
* $FD = \mathbf{7}$ cm
* $\angle C = \angle F = \mathbf{80}^\circ$
* $\angle F = \mathbf{80}^\circ$

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Problem 2: $\triangle GHI \cong \triangle JKL$

Matching Parts:
* Angle $G$ corresponds to Angle $J$.
* Angle $H$ corresponds to Angle $K$.
* Angle $I$ corresponds to Angle $L$.
* Side $GH$ corresponds to Side $JK$.
* Side $HI$ corresponds to Side $KL$.
* Side $IG$ corresponds to Side $LJ$.

Finding Values from the Diagrams:
* From $\triangle GHI$: Side $GH = 18$ in, Side $HI = 13$ in, Side $IG = 12$ in.
* From $\triangle JKL$: Angle $J = 90^\circ$, Angle $K = 30^\circ$, Angle $L = 60^\circ$.

Filling in the blanks:
* $GH = JK = \mathbf{18}$ in
* $JK = \mathbf{18}$ in
* $\angle G = \angle J = \mathbf{90}^\circ$
* $\angle J = \mathbf{90}^\circ$
* $HI = KL = \mathbf{13}$ in
* $KL = \mathbf{13}$ in
* $\angle H = \angle K = \mathbf{30}^\circ$
* $\angle K = \mathbf{30}^\circ$
* $IG = LJ = \mathbf{12}$ in
* $LJ = \mathbf{12}$ in
* $\angle I = \angle L = \mathbf{60}^\circ$
* $\angle L = \mathbf{60}^\circ$

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Problem 3: $\triangle MNO \cong \triangle PQR$

Matching Parts:
* Angle $M$ corresponds to Angle $P$.
* Angle $N$ corresponds to Angle $Q$.
* Angle $O$ corresponds to Angle $R$.
* Side $MN$ corresponds to Side $PQ$.
* Side $NO$ corresponds to Side $QR$.
* Side $OM$ corresponds to Side $RP$.

Finding Values from the Diagrams:
* From $\triangle MNO$: Side $MN = 12$ cm, Angle $M = 40^\circ$, Angle $N = 60^\circ$.
* *Calculation:* The angles in a triangle add up to $180^\circ$. So, Angle $O = 180^\circ - 40^\circ - 60^\circ = \mathbf{80^\circ}$.
* From $\triangle PQR$: Side $RP = 14$ cm.

Filling in the blanks:
* $MN = PQ = \mathbf{12}$ cm
* $PQ = \mathbf{12}$ cm
* $\angle M = \angle P = \mathbf{40}^\circ$
* $\angle P = \mathbf{40}^\circ$
* $NO = QR$ (We don't have this specific length labeled on either triangle, so we leave it as the variable name or check if implied. Looking closely at the image, there is no number for side NO or QR. However, usually, these worksheets ask for values found in the diagram. Let's look at the other sides).
* Wait, let's re-read the diagram carefully.
* Triangle MNO has side MN=12, angle M=40, angle N=60.
* Triangle PQR has side RP=14, angle R is not labeled but corresponds to O (which is 80), angle Q corresponds to N (which is 60), angle P corresponds to M (which is 40).
* Side OM corresponds to Side RP. Since $RP = 14$, then $OM = 14$.
* Side NO corresponds to Side QR. Neither has a value given in the diagram. In many of these problems, if a value isn't there, you might just write the corresponding side name or it's a trick question. However, looking at the pattern, usually all blanks have numbers. Let me re-examine the image. Ah, I see "14 cm" next to side RP (or PR). And "12 cm" next to MN. There is no label for NO/QR or MO/PR? No, MO corresponds to PR. PR is 14. So MO is 14.
* Is there a label for NO? No. Is there a label for QR? No.
* Let's check the angles again.
* $\angle N = 60^\circ$, so $\angle Q = 60^\circ$.
* $\angle O = 80^\circ$ (calculated), so $\angle R = 80^\circ$.

Let's fill what we know for sure:
* $MN = PQ = \mathbf{12}$ cm
* $PQ = \mathbf{12}$ cm
* $\angle M = \angle P = \mathbf{40}^\circ$
* $\angle P = \mathbf{40}^\circ$
* $NO = QR$ (Value unknown from diagram)
* $QR$ (Value unknown from diagram)
* $\angle N = \angle Q = \mathbf{60}^\circ$
* $\angle Q = \mathbf{60}^\circ$
* $OM = RP = \mathbf{14}$ cm
* $RP = \mathbf{14}$ cm
* $\angle O = \angle R = \mathbf{80}^\circ$
* $\angle R = \mathbf{80}^\circ$

*Self-Correction on Problem 3:* Often in these sheets, if a side length is missing from the diagram, it might be impossible to fill with a number. However, looking at the layout, $NO$ and $QR$ are the only ones without explicit numbers. I will provide the known numbers and note the correspondence for the missing lengths.

Final Answer:

1. $\triangle ABC \cong \triangle DEF$
* $AB = \mathbf{15}$ cm, $DE = \mathbf{15}$ cm, $\angle A = \mathbf{40}^\circ$, $\angle D = \mathbf{40}^\circ$
* $BC = \mathbf{12}$ m, $EF = \mathbf{12}$ m, $\angle B = \mathbf{60}^\circ$, $\angle E = \mathbf{60}^\circ$
* $CA = \mathbf{7}$ cm, $FD = \mathbf{7}$ cm, $\angle C = \mathbf{80}^\circ$, $\angle F = \mathbf{80}^\circ$

2. $\triangle GHI \cong \triangle JKL$
* $GH = \mathbf{18}$ in, $JK = \mathbf{18}$ in, $\angle G = \mathbf{90}^\circ$, $\angle J = \mathbf{90}^\circ$
* $HI = \mathbf{13}$ in, $KL = \mathbf{13}$ in, $\angle H = \mathbf{30}^\circ$, $\angle K = \mathbf{30}^\circ$
* $IG = \mathbf{12}$ in, $LJ = \mathbf{12}$ in, $\angle I = \mathbf{60}^\circ$, $\angle L = \mathbf{60}^\circ$

3. $\triangle MNO \cong \triangle PQR$
* $MN = \mathbf{12}$ cm, $PQ = \mathbf{12}$ cm, $\angle M = \mathbf{40}^\circ$, $\angle P = \mathbf{40}^\circ$
* $NO = QR$ (length not given in diagram), $\angle N = \mathbf{60}^\circ$, $\angle Q = \mathbf{60}^\circ$
* $OM = \mathbf{14}$ cm, $RP = \mathbf{14}$ cm, $\angle O = \mathbf{80}^\circ$, $\angle R = \mathbf{80}^\circ$