Congruent Triangles 1
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Question 1 of 4
1. Question
Is `∆XYU` congruent to `∆ZUW`Hint
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `XU``=``UW`Reason: Given by the markings (two dashes) on each segment`(S)` SideStatement: `/_ XUY``=``/_ ZUW`Reason: Vertically Opposite angles are equal`(A)` AngleWe have proved congruence of `1` side and `2` angles between the two triangles. Therefore, the two triangles are congruent according to the AngleAngleSide `\text((AAS))` criteriaYes, `∆XYU` is congruent to `∆ZUW`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:SideSideSide `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.SideAngleSide `\text((SAS))`
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the otherAngleAngleSide `\text((AAS))`
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.Right AngleHypotenuseSide `\text((RHS))`
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of anotherAlternate, Corresponding and CoInterior Angle TypesAlternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.CoInterior Angles
CoInterior Angles are when two angles have a sum of `180°.` These angles typically form a C Shape 
Question 2 of 4
2. Question
Is `∆XYW` congruent to `∆YZW`Hint
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `XY``=``YZ`Reason: Given by the markings (two dashes) on each segment`(S)` SideStatement: `XW``=``WZ`Reason: Given by the markings (one dash) on each segment`(S)` SideStatement: `YW``=``YW`Reason: This is a common side for both triangles`(S)` SideWe have proved congruence of `3` sides angles between the two triangles. Therefore, the two triangles are congruent according to the SideSideSide `\text((SSS))` criteriaYes, `∆XYW` is congruent to `∆YZW`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:SideSideSide `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.SideAngleSide `\text((SAS))`
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the otherAngleAngleSide `\text((AAS))`
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.Right AngleHypotenuseSide `\text((RHS))`
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of anotherAlternate, Corresponding and CoInterior Angle TypesAlternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.CoInterior Angles
CoInterior Angles are when two angles have a sum of `180°.` These angles typically form a C Shape 
Question 3 of 4
3. Question
Is `∆AED` congruent to `∆EBC`Hint
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `AE``=``EC`Reason: Given by the markings (two dashes) on each segment`(S)` SideStatement: `/_ AED``=``/_ BEC`Reason: Vertically Opposite angles are equal`(A)` AngleStatement: `DE``=``EB`Reason: Given by the markings (one dash) on each segment`(S)` SideWe have proved congruence of `2` sides and `1` angle between the two triangles. Therefore, the two triangles are congruent according to the SideAngleSide `\text((SAS))` criteriaYes, `∆AED` is congruent to `∆EBC`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:SideSideSide `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.SideAngleSide `\text((SAS))`
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the otherAngleAngleSide `\text((AAS))`
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.Right AngleHypotenuseSide `\text((RHS))`
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of anotherAlternate, Corresponding and CoInterior Angle TypesAlternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.CoInterior Angles
CoInterior Angles are when two angles have a sum of `180°.` These angles typically form a C Shape 
Question 4 of 4
4. Question
Is side `BC` equal to side `EF`Hint
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Two triangles are congruent if all corresponding angles and sides are equalUse the given diagram to determine whether any of the angles or sides are congruentStatement: `/_ A``=``/_ D`Reason: Given by the values (`55°`) on each segment`(A)` AngleStatement: `/_ C``=``/_ F`Reason: Given by the values (`65°`) on each segment`(A)` AngleStatement: `AB``=``ED`Reason: Given by the markings (one dash) on each segment`(S)` SideWe have proved congruence of `2` angles and `1` side between the two triangles. Therefore, the two triangles are congruent according to the AngleAngleSide `\text((AAS))` criteriaSince we have proven the congruence of the two triangles, it means that corresponding sides, such as sides `BC` and `EF`, are equal.Yes, side `BC` is equal to side `EF`More InfoCongruent TrianglesUse any of the following 4 tests to prove congruence between two triangles:SideSideSide `\text((SSS))`
If 3 sides of one triangle are equal to 3 sides of another triangle, then the triangles are congruent.SideAngleSide `\text((SAS))`
Two triangles are congruent if 2 sides and the included angle of one are respectively equal to 2 sides and the included angle of the otherAngleAngleSide `\text((AAS))`
Two triangles are congruent if 2 angles and a side of one are respectively equal to 2 angles and the corresponding side of the other.Right AngleHypotenuseSide `\text((RHS))`
Two right angled triangles are congruent if the hypotenuse and a side of one are respectively equal to the hypotenuse and a side of anotherAlternate, Corresponding and CoInterior Angle TypesAlternate Angles
Alternate Angles in parallel lines are equal. These angles typically form a Z shape.Corresponding Angles
Corresponding Angles in parallel lines are equal. These angles typically form an F shape.CoInterior Angles
CoInterior Angles are when two angles have a sum of `180°.` These angles typically form a C Shape