Day 1: Triangle Inequality & Side/Angle Relationships
1. Can a triangle have sides with the given lengths? Explain why or why not.
a) 7, 8, 14
b) 6, 9, 15
c) 21, 15, 5
2. Two sides of a triangle have lengths 10 and 17. Find the range for the possible length of the third side.
3. In \( \triangle ABC \), list the sides in order from shortest to longest if \(m\angle A = 58^\circ\), \(m\angle B = 62^\circ\), and \(m\angle C = 60^\circ\).
4. In \( \triangle XYZ \), list the angles in order from smallest to largest if \(XY = 12\), \(YZ = 15\), and \(XZ = 9\).
Day 2: Triangle Angles
5. Find the value of x in the triangle with angles: \( x^\circ, 85^\circ, 40^\circ \).
6. Find the measure of the exterior angle if the two remote interior angles are \( 50^\circ \) and \( 70^\circ \).
7. Find the value of x if the exterior angle is \( (5x-10)^\circ \) and the remote interior angles are \( (2x)^\circ \) and \( (x+20)^\circ \).
8. An isosceles triangle has two base angles measuring \( (3x+5)^\circ \) and a vertex angle of \( (2x)^\circ \). Find the measure of all three angles.
Day 3: Proving Triangles Congruent
9. State if the two triangles are congruent. If they are, state how you know (SSS, SAS, or ASA).
a) Two triangles share a side. The other two pairs of sides are marked as congruent.
b) Two triangles have two pairs of corresponding angles and the included side marked as congruent.
c) Two triangles have two pairs of corresponding sides and the non-included angle marked as congruent.
10. What additional information is required in order to know that the triangles are congruent for the reason given?
a) ASA, given two pairs of congruent angles.
b) SSS, given two pairs of congruent sides.
c) SAS, given one pair of congruent sides and one pair of congruent angles.
Day 4: Congruence with Algebra & Coordinates
11. Given \( \triangle GHI \cong \triangle JKL \), \( GH = 2y - 5 \), \( JK = 15 \), and \( m\angle I = (x+10)^\circ \), \( m\angle L = 65^\circ \). Find x and y.
12. Given \( \triangle ABC \cong \triangle DEF \), \( m\angle A = (5x)^\circ \), \( m\angle D = (3x+20)^\circ \), \( BC=y-2 \), and \( EF=10 \). Find x and y.
13. Use the distance formula to prove that \( \triangle ABC \cong \triangle DEF \). Show all work.
A(0, 5), B(0, 0), C(3, 0)
D(8, 5), E(8, 0), F(5, 0)
14. Use the distance formula to determine if \( \triangle PQR \cong \triangle STU \). Show all work.
P(-1, 2), Q(-1, 5), R(-4, 2)
S(3, 1), T(3, 4), U(1, 1)