1) Problem: Given that \(\triangle ABC \cong \triangle DEF\), answer the following: 1.a) Find the sequence of rigid transformations that take \(\triangle ABC\) to \(\triangle DEF\). Step 1: Identify corresponding vertices: \(A \leftrightarrow D\), \(B \leftrightarrow E\), \(C \leftrightarrow F\). Step 2: Determine transformations such as translation, rotation, and/or reflection that map \(\triangle ABC\) onto \(\triangle DEF\). For example, a possible sequence is: - Translate \(\triangle ABC\) so that point \(A\) coincides with point \(D\). - Rotate around point \(D\) to align side \(AB\) with side \(DE\). - Reflect if necessary to match orientation. 1.b) What is the image of segment \(BC\) after the transformation? Since \(B\) maps to \(E\) and \(C\) maps to \(F\), segment \(BC\) maps to segment \(EF\). 1.c) Explain how you know those segments are congruent. By the definition of congruent triangles, corresponding sides are congruent. Since \(\triangle ABC \cong \triangle DEF\), segment \(BC \cong EF\). 2) Problem: Describe each rigid transformation in the sequence of quadrilateral JKLM. 2.a) Quad JKLM is mapped onto Quad J'K'L'M' by a __reflection__ (or rotation/translation depending on the figure). 2.b) Quad J'K'L'M' is mapped onto Quad J"K"L"M" by a __translation__ (or rotation/reflection depending on the figure). 2.c) \(\angle L\) matches with \(\angle L'\) and \(\angle L''\) depending on the transformations. 2.d) Segment \(K''J'' \cong K'J' \cong KJ\) by congruence of rigid transformations. 2.e) The statement "Segment JK is congruent to Segment K'J'" is wrong if the order of points is reversed, because congruence depends on corresponding points and orientation. 3) Problem: Triangle FGH is the image of isosceles triangle FEH after reflection across line HF. Select all true statements: - \(\square\) EFGH is a rectangle: False (no evidence). - \(\square\) EFGH has 4 congruent sides: False. - \(\checkmark\) Diagonal FH is perpendicular to side FE: True, since reflection across HF implies \(FH\) is axis and perpendicular. - \(\checkmark\) Angle FEH is congruent to angle FGH: True by reflection. - \(\checkmark\) Angle EHG is congruent to Angle HGF: True by reflection. 4) Problem: Given triangle ABC with right angle at B. 4.a) Sketch the reflection of \(\triangle ABC\) across line BC. Reflection across BC maps point A to A' such that BC is the axis. 4.b) Is triangle ACA' scalene, isosceles, or equilateral? Explain. Triangle ACA' is isosceles because A and A' are symmetric about BC, so \(AC = A'C\). 5) Problem: Rectangle ABCD is reflected across line EF, image is DCBA. Explain why segment AB is congruent to segment DC. By properties of rectangles, opposite sides are congruent. Reflection preserves lengths, so \(AB \cong DC\).