Math

QuestionTriangle ABC\mathrm{ABC} a AB=6 cm\mathrm{AB}=6 \mathrm{~cm}, BC=3 cm\mathrm{BC}=3 \mathrm{~cm}, AC=4 cm\mathrm{AC}=4 \mathrm{~cm}. Trouvez M, Q, et analysez le triangle MABMAB.

Studdy Solution

STEP 1

Assumptions1. ABC is a triangle with AB =6 cm, BC =3 cm, and AC =4 cm. . Line (d) is the perpendicular bisector of line segment [AB] and intersects line segment [BC] at point M.

STEP 2

To construct the figure, we first draw triangle ABC with the given side lengths.

STEP 3

Next, we construct line (d), the perpendicular bisector of line segment [AB]. To do this, we find the midpoint of [AB] and draw a line through this point that is perpendicular to [AB]. This line intersects [BC] at point M.

STEP 4

To determine the nature of triangle MAB, we examine the lengths of its sides. Since line (d) is a perpendicular bisector of [AB], we know that AM = MB. Therefore, triangle MAB is an isosceles triangle.

STEP 5

Next, we draw the height from point C to line segment [AB]. This line segment intersects [AB] at point Q.

STEP 6

To determine the relationship between lines (d) and (CQ), we note that line (d) is a perpendicular bisector of [AB] and line (CQ) is a height from point C to line segment [AB]. Therefore, lines (d) and (CQ) are both perpendicular to [AB].

STEP 7

Since both lines are perpendicular to the same line, they are parallel to each other. Therefore, lines (d) and (CQ) are parallel.

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