Question

unit 3 worksheet tr1: test review
classify triangles: classify the triangles by its sides and by its angles.
1)
sides: _______ angles: _______
2)
sides: _______ angles: _______
3)
sides: _______ angles: _______
4)
sides: _______ angles: _______
determine if the triangles are congruent. if they are, name the triangles and state the reason.
5)
congruent? y or n
△mat≅△_________
by _________
6)
congruent? y or n
△got≅△_________
by _________
7)
congruent? y or n
△pay≅△_________
by _________

Explanation:

Step 1: Classify triangle 1

• Sides: Two sides are marked equal (isosceles triangle property).
• Angles: All angles are less than \(90^{\circ}\) (acute triangle property).

Step 2: Classify triangle 2

• Sides: No sides are marked equal (scalene triangle property).
• Angles: One angle (\(100^{\circ}\)) is greater than \(90^{\circ}\) (obtuse triangle property).

Step 3: Classify triangle 3

• Sides: All sides are marked equal (equilateral triangle property).
• Angles: All angles are equal (\(60^{\circ}\), equiangular triangle property).

Step 4: Classify triangle 4

• Sides: No sides are marked equal (scalene triangle property).
• Angles: One angle is \(90^{\circ}\) (right - triangle property).

Step 5: Check congruence for triangle 5

• Congruence: \(\triangle MAT\) and \(\triangle MHT\) have two sides and included angle equal (SAS congruence).

Step 6: Check congruence for triangle 6

• Congruence: \(\triangle GOT\) and \(\triangle AOT\) have right angle, hypotenuse and one side equal (HL congruence).

Step 7: Check congruence for triangle 7

• Congruence: \(\triangle PAY\) and \(\triangle RAT\) have two angles and included side equal (ASA congruence).

Answer:

1. Sides: C (Isosceles), Angles: E (Acute)
2. Sides: B (Scalene), Angles: F (Obtuse)
3. Sides: A (Equilateral), Angles: D (Equiangular)
4. Sides: B (Scalene), Angles: G (Right)
5. Congruent? Y, \(\triangle MAT\cong\triangle MHT\), By SAS
6. Congruent? Y, \(\triangle GOT\cong\triangle AOT\), By HL
7. Congruent? Y, \(\triangle PAY\cong\triangle RAT\), By ASA