Lesson Worksheet: Applications on Congruent Triangles Mathematics • 8th Grade

In this worksheet, we will practice identifying congruence in triangles using different criteria of SSS, SAS, and ASA and using this to find unknown angles or sides.

Q1:

Are two triangles congruent if both triangles have the same side lengths?

  • ANo
  • BYes

Q2:

In the given figure, △𝐴𝐡𝐢≅△𝐿𝑀𝑁. Determine π‘šβˆ π‘.

Q3:

In the following figure, find π‘šβˆ π½πΎπΏ.

Q4:

Given that △𝐹𝐺𝐻≅△𝐾𝐿𝑀, π‘šβˆ πΉ=83∘, and π‘šβˆ π»=83∘, determine π‘šβˆ πΏ.

Q5:

Determine the value of π‘₯ in the given congruent triangles.

Q6:

In the following figure, find π‘šβˆ π‘ƒπ‘„π‘†.

Q7:

Given that △𝑅𝑆𝑉≅△𝑇𝑉𝑆, find the values of π‘₯ and 𝑦.

  • Aπ‘₯=61, 𝑦=46
  • Bπ‘₯=29, 𝑦=38
  • Cπ‘₯=29, 𝑦=46
  • Dπ‘₯=61, 𝑦=23
  • Eπ‘₯=29, 𝑦=23

Q8:

In the figure, 𝐡𝐷 meets 𝐴𝐸 at 𝐢, which is also the midpoint of 𝐡𝐷. Find the length of 𝐢𝐸.

Q9:

Given that β–³π΄π΅πΆβ‰…β–³π‘‹π‘Œπ‘, and π‘šβˆ π΄+π‘šβˆ π΅=117∘, what is π‘šβˆ π‘?

Q10:

Given that 𝐴𝐡𝐢𝐷 is a square, find π‘šβˆ π‘ŒπΆπ΅.

Q11:

From the information in the figure, what is π‘šβˆ π΅π‘€πΆ?

Q12:

In the figure below, π·π‘‹π‘ŒπΈ is a rectangle. Find π‘šβˆ π΄πΈπ·.

Q13:

Triangles 𝐴𝐡𝐢 and 𝐸𝐷𝐹 are congruent. What is the perimeter of △𝐴𝐡𝐢?

Q14:

Consider the figure, then complete the following using <, =, or >: π‘‹π‘Œπ‘‹π‘Š.

  • A<
  • B=
  • C>

Q15:

Given that 𝐡𝐢=𝐴𝐷, 𝐴𝐢=𝐴𝐸, and π‘šβˆ πΆπ΄π΅=68∘, find π‘šβˆ πΈπ΄π·.

Q16:

Given that △𝐴𝐸𝐢 and △𝐡𝐹𝐷 are congruent, what is the measure of ∠𝐡𝐷𝐹?

Q17:

Given that triangle 𝐴𝐡𝐢 is congruent to triangle π‘‹π‘Œπ‘, find π‘šβˆ π΅.

  • A52∘
  • B74∘
  • C42∘
  • D54∘

Q18:

Find π‘šβˆ π΅π΄πΈ.

Q19:

The two triangles in the given figure are congruent. Work out the area of triangle 𝐴𝐡𝐢.

Q20:

If △𝐴𝐡𝐢≅△𝐴𝐡𝐷, the perimeter of 𝐴𝐢𝐡𝐷=394cm, and 𝐴𝐡=56cm, find the perimeter of △𝐴𝐡𝐢.

Q21:

Given that △𝐴𝐡𝐢≅△𝐴𝐡𝐷, find the perimeter of 𝐴𝐢𝐡𝐷.

Q22:

Given that △𝐴𝐡𝐢 is congruent to β–³π‘‹π‘Œπ‘, first find the length in β–³π‘‹π‘Œπ‘ that is equal to 𝐴𝐡. Then find the angle in △𝐴𝐡𝐢 with the same measure as βˆ π‘.

  • Aπ‘Œπ‘, ∠𝐡
  • Bπ‘‹π‘Œ, ∠𝐢
  • C𝑋𝑍, ∠𝐴

Q23:

In the figure, △𝐴𝐡𝐢 and △𝐸𝐹𝐷 are congruent.

Work out the length of 𝐡𝐢.

Work out the length of 𝐸𝐹.

Work out the measure of angle 𝐷𝐸𝐹.

Q24:

In the figure shown, π‘šβˆ π΅π·πΈ=50∘. What is π‘šβˆ πΈπ΄πΆ?

Q25:

Suppose β–³π΄π΅πΆβ‰…β–³π‘‹π‘Œπ‘. If the perimeter of △𝐴𝐡𝐢 is 14, π‘‹π‘Œ=3, and π‘Œπ‘=5, what is 𝐴𝐢?

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